I just saw your post or I would have responded sooner, sorry about that...I have had my Blue Quaker, Lita, for over 2 years now, and I got her as a just-weaned, 10-week old baby from a private breeder who has been breeding them for decades. She had a lot of breeders and she allowed me to check-out her breeder-bird room, which is rare, usually people do not allow others in to see their breeder-birds, as they worry about illnesses and such, but I drove 4 hours to pick her up, so she allowed me to check them all out. She is a breeder of all mutations/colors, she had Greens, Blues, and Yellows, and then Dilutes of each color as well. They were all gorgeous. She pulls her chicks from the nest-box between 2-3 weeks old, and all of her babies were absolutely the most cuddly, friendly little baby birds I've ever interacted with. You could tell that she spends ample time with her babies every single day, and she even gets them all used to both flight-suits and the Aviator Harnesses. So as a result, Lita is by-far the most tame, laid-back bird in my flock, and that I've ever owned (my flock includes a Senegal, a Yellow-Sided Green Cheek, a Cockatiel, and English/American Budgies which I bred)...
The reason I'm telling you this is that from everything that I had read about Quaker Parrots over the years, prior to getting one, they do have a tendency to become or just be a bit nippy and most of all stubborn and bull-headed. The reason that I wanted one, besides that I wanted a bit larger bird with a large-parrot attitude/intelligence in a smaller bird package, was that I just loved their attitudes, they are very loving but don't take any crap!!! They set-up shop wherever they want to and can survive the Northeast winters in Brooklyn, Rhode Island, New Jersey, etc. And after going to Coney Island and other spots in Brooklyn to see the resident Quaker colonies that have resided there for decades, I was hooked!
Lita isn't at all like the descriptions I have heard other people give of their Quaker Parrots, neither on here, in-person, or in the many YouTube videos I've watched of them posted by their owners. Most of them are very intelligent and can be extremely loving and cuddly when they want to be, but they all seem to have such a bull-headed streak in them that they tend to rule-the-roost because their owners don't start training them as soon as they bring them home and into their families, and that is what I think the key to getting rid of that nippy-streak is. Well, that and making sure that you find a reputable, private breeder who pulls their babies from the parents between 2-3 weeks old, NO OLDER, and that hand-raises/hand-feeds them, but who also spends a ton of time with their babies, handling and closely and personally interacting with them...As a former breeder I can tell you that a lot of breeders who do hand-raise/hand-feed their babies ONLY do just that, they pull them from their parents at the correct age (no younger than 2 weeks old and no older than 3 weeks old), and then they hand-feed them on a proper schedule, and then they Abundance-Wean them in a proper weaning-cage...But they don't spend any extra time with them at all, let alone on a daily basis, handling them, touching them under and on their wings, holding their wings out, putting them on their backs and touching their feet, etc. And if you can ask them and get them to start putting the Aviator Harness on the baby you pick-out, then that's a bonus.
Lita has never once bitten me hard or with malice...Quakers are "beakers", meaning that they gently and very lightly beak you all the time, it's a friendly, loving thing, not a malicious thing, and has nothing to do with biting. All birds do it, but Quakers do it constantly. Lita absolutely loves attention, and is such a good, well-behaved girl. While my Green Cheek Conure climbs all over me, chewing on any part of me he can get a hold of, lol, and is always getting into something, Lita is content to sit on my shoulder and snuggle. She does the typical "Quaker Marching" back and forth, it's hilarious, they look just like little soldiers! And she is by-far the clown of the flock, all Quakers are little clowns, and they absolutely love to dance to music, or just your singing!!! If I sing one line to a song Lita starts dancing, she also head-bangs, full on head-bangs...
Now the one con that I can give you about Quakers...THEY ARE LOUD! And I mean they are loud...they scream quite a bit, I don't know if this is a general rule, but from what I've seen of other Quakers, it's pretty universal. They make all kinds of very unique Quaker noises, of course they do the "Quaking" noise, but they do scream quite a bit to simply communicate...So if loudness is a problem for you or where you live, then it will be extremely important for you to keep ample toys, foraging activities (she loves to rip things apart and shred things), and give your Quaker at the very least 5-6 hours a day out of their cage time. At first Lita would scream for me constantly, even when I'd let her out of her cage in the "bird room" of my house, if I wasn't there she would scream and scream, and even if I called back to her to let her know where I was, she just would scream and scream until I came back into the room with her. It wasn't that she wanted me to be directly interacting with her or playing with her, she just wanted me in the same room with her, and once I was she would then stop screaming and entertain herself with her toys. So I did 2 different things that stopped the screaming: #1) I built 2 different Bird-Stands out of PVC piping and fittings; one was just a simple T-Stand that is about 5 feet tall and has a food dish and a water dish built-into it, and then below the top perch where the bowls are I put a second tier perch and drilled/attached an S-hook to the underside of the top perch so that a toy could be hung down from it, so she could go to the lower perch when she wanted to and play with the toy, and then the second stand is actually a massive bird-gym, complete with a built-in swing, tons of different perches to walk on/climb up, and tons of toys hanging all over it, along with different ropes hanging from it that go to the floor and all over the gym for them to climb on. The big gym stays in the "bird-room", and the T-Stand goes to whatever room I'm going to be in when I'm home. So while my other birds are content to be in the bird-room playing on the gym, Lita typically comes to whatever room I'm in and sits on the T-Stand, and doesn't scream....#2) I moved her main-cage to the living room, which is where I spend most of my time, as I have an open downstairs, with the living room, kitchen, and dining room all open to each other. So whether I'm cooking, watching TV, playing a video game, on the computer, reading, etc., she can be in her cage entertaining herself and is content that I'm still within sight of her...and if she still screams, then she comes out on the T-Stand...usually all of my birds are out if I'm home anyway...
As far as an Indian Ringneck goes, I've never personally owned one myself, but I know 2 people/couples that have one currently (one has to be at least 10 years old now, and they've had him since he was a baby), and I've spent ample time with both Indian Ringnecks and Alexandrines at the Avian Rescue I volunteer for...If I'm being truthful with you, when I first started thinking about getting another parrot, I too had narrowed it down to either a Quaker or an IRN/Alexandrine...I guess your decision all depends on what you want in a pet parrot. A lot of people will tell you that the Ringnecks are not really "cuddly" birds, I've heard that several times and read it quite often, but one of the friend's of mine who have one seem to have a very cuddly one. So it's just like anything else, it depends on the bird and how they are raised and how much they are interacted with on a daily basis, and the type of living environment you keep them in.
I would say that as far as kids go, as long as you are going the route of bringing home a hand-raised baby and not an adult bird that needs some training, then I wouldn't worry about your kids interacting with either species. And I'm all-for adopting an adult parrot from a rescue and committing yourself to working with them every day in order to tame them/train them, but as far as young kids go, who are going to want to touch the bird and interact with the bird, and where you worry about fingers and toes and faces/eyes, bringing home a very tame, hand-raised/hand-fed baby that has just weaned is probably the best route to go, not only for safety purposes, but also so that your baby bird can actually grow-up with your kids.