Parrotlets are super cute! I don't know much about their nature, but I do hear a lot that they're big parrots in a little body. I love some of their color mutations.
The Senegal (and related family) would not be a good choice for a family with small children. Besides having a pretty hardwired drive towards one person-ness regardless of socialzation, they have a large beak for the body size as you already know

and are very hard biters. It's not just a phase, any long time Poicephalus owners can tell you they will bite unexpectedly sometimes. They're awesome birds for adult owners who are aware of their tendencies.
Have you considered the smaller conures that are very popular nowdays? GCC come in many beautiful color mutations. Love being social, and from what I hear, can be trained fairly easily, and trained out of biting fairly easily too. Then there's Sun conures, Jenday, Nanday, Gold Cap and more... those are pretty LOUD though and can be irritating to some people

.
Did you not want a Cockatiel? I know you mentioned your husband had them before. They make nice family pets, and especially the females are known to be gentle and friendly.
IRN? (Indian Ringneck), they're popular and beautiful birds, and come in many different colors. I don't think they bond super tightly to one person, but they're also not known to be hands-on cuddly. They need consistent socialization to keep them tame and handleable. They're in the size range you're looking for.
Oh, and I love my English Budgie

. They are typically almost twice, to twice the size of a common budgie. I have sweet breeder raised handfed girl. She's smart too, just like a little parrot!
Good luck...