Hi Jenn...I'm sorry that this is happening to you...I'm assuming that these guys were a parent-raised, non-tame breeding-pair prior to you adopting them? Are you able to handle them or interact with them at all when they are not nesting? It's normal for them to protect the dead chick, eggs, etc., and it is the right thing to do to let them realize that the chick is dead and until they lose interest...HOWEVER...
With some parrots they already know the chick is dead, but they will still be aggressive and want to keep it away from anything and everything forever...Obviously you cannot let the dead chick in their cage much longer, as once it starts to decompose it is unhealthy for them, you, etc. You will have not only bacteria, fungi, etc. all through their cage and your home, but also insects, even if it is winter where you live...That's how decomp works...So if they don't stop protecting the dead chick within another day or so, you just have to get it out of there somehow, because it does and will get to the point where it's totally unhealthy for everyone...
I have seen this happen a few times over the years with breeding-pairs who have been surrendered to the Avian Rescue I work for, and there was a breeding-pair of Orange-Winged Amazons who did this, and their owners didn't know what to do so they decided to dump them inside of their cage on our doorstep...And I just put on a pair of welder's gloves (this was a non-tame, typical breeding-pair of parrots who wanted nothing to do with people, certainly not people inside of their cage), and I covered my arms with several layers of sleeves with the welder's gloves going up over my elbows almost to my shoulders (thank god), opened the cage just far enough to get my hand/arm inside, kept my face/head outside of the cage and turned away from their direction, and just hurried up and grabbed the dead chick and yanked it out...That's how I typically get eggs they lay occasionally out too if they are a non-tame breeding-pair that you can't handle...Then we boil the eggs and put them right back in after they cool-down, and do this with each egg they lay in a clutch...And eventually they do lose interest in the eggs. That takes about a week or two AFTER the typical incubation period, when they finally realize the eggs aren't going to hatch for them to stop laying on them...And they typically won't start laying on the eggs until at least 2 are laid, which is totally normal...
***I don't know the history of your birds, whether they were pets or breeder's in their prior life, but it sounds like you adopted a non-tame breeding-pair of parrots...You can't separate them because with Macaws it will only result in two very aggressive, depressed birds that will both be plucking, self-mutilating, screaming, etc. So that's not an option...But what you do need to do is modify their environment, their diet, etc. so that nothing is causing them to be hormonal and encouraging them to breed. It is very possible to have a non-tame, bonded breeding-pair of parrots living together inside of the same cage that do not breed...But it's going to be up to you guys to know the do's and don't's of that and stick to the rules...
I've seen former breeding-pairs of parrots who were parent-raised and never tame turn into very sweet pet parrots...But it take a lot of work, and most of all patience and time. I don't know what your goal for these birds is, but you definitely need to remove any and all boxes of any kind, and eliminate any and all small, dark places that either of the can get into or underneath...NEVER any nest-boxes, cardboard boxes, blankets, towels, any types of "bedding" like wood-chips, shredded paper, etc. Nothing that can be used as nesting material. Always allow any eggs that are laid to simply lay on the bottom grate of the cage, never put them in any type of "nest". No Huts, tents, hammocks, or "beds" of any kind.
Also, they need to be on a "Natural Light Schedule" for sure...If you use the search function here on the forum and search of that, you will find many posts with detailed explanations of what a "Natural Light Schedule" is...Basically it means that their cage needs to be in an area/room with a window so that they can see the natural light changes at both sunrise and sunset, and they need to wake with sunrise as they see it happen (which they typically do anyway unless they are covered at night, if they are covered then the cover must be removed right at sunrise), and then they need to be able to watch the sunset and then go to sleep right as they watch the sunset. So if you cover them for bed, that means allowing them to watch the light changes that naturally occur with sunset, and then cover them right after the sun sets...This means that depending on the time of the year, they are going to be going to bed at 9:00 at night in the summer, and 5:30 at night in the winter...But this is EXACTLY what birds do naturally in the wild...ALL BIRDS...This is why we hear birds start chirping in the morning as soon as the sun rises, and we don't hear any birds chirping or see them flying after sunset (except for nocturnal birds like owls of course)...After about a month of getting them on a Natural Light Schedule their hormones will calm and their mating behaviors will cease, but you have to be extremely strict about keeping them on that schedule, and changing that schedule as the seasons change and the time of sunrise and sunset changes.
Also there is their daily diet...What is their normal, daily diet? You need to always avoid all warm, mushy foods, such as hand-feeding formulas, oatmeal, grits, mashed potatoes, anything of that consistency...
***Once they lay their first egg, that's when the danger of them laying egg after egg after egg begins, so if this continues, you should probably consider getting your female to a Certified Avian Vet and having Deslorelin/Suprelorelin Implants put in to shut-down her Reproductive System. That's really the only sure way to keep her healthy and from being bred to death or laying eggs to the point that she is malnourished and emaciated, or before she becomes egg-bound...Make sure that there is always a large Avian Mineral-Block hanging in their cage for her, as she needs the extra Calcium and Phosphorous. You can order them online, or all Petco's sell a pretty large yellow-colored Avian Mineral Block that is shaped like a flower that would be the right size for a Macaw. Also, offering her small dish of Egg-Food during and for a week after she lays an egg will also help to replenish her calcium and the calories she's used. You can buy a bag of Qwiko Egg-Food also at any Petco for $10.
Parrots are not like any other "exotic" animals, and breeding parrots and their hormonal behaviors/activities are nothing like any other "exotics" at all...So it's a very unique, confusing, and very often frustrating process. And there is a TON of very bad information on the internet about this topic, so you also have to be very careful to filter through the BS and not do anything that is going to make the situation worse...You've found by-far the most educated, experienced parrot forum on the internet, so please do not ever hesitate to ask any and all questions that you have...We're all here to help.