Every bird is an individual, so it's hard to make species specific recommendations. With little kids, I would shy away from any potentially phobic or mellow species - they tend not to do well with all the screaming and fast movements of little kids, so that's poi's, eclectus, etc. You want something with a stable, gregarious personality that will go to all the kids and be gentle. You're a stay at home mom, yea? Have you considered cockatoos? If you stay at home, and keep a nice routine, a cockatoo can fit in very nicely. You would have the time to dedicate and the kids would be relatively safe handling them since they're a more mellow species, generally.
The bigger 'toos tend to be the more mellow, I'm thinking specifically of umbrellas
However, a goffins or lesser sulfur crested is a good size, still very snuggly and hands on, but also hyper little puff balls, so will want to bounce, play, run around, come to get a snuggle or two, then bounce off to the next adventure
They're very smart, can be decent talkers. Not super clear, but can learn quite a few words. They can be needy, but if you keep a regular schedule and routine, include the bird in your daily life, they settle in quite well. The key is to have the cage in a central area where they can still see everyone and feel like they are a "part of the flock" as well as letting them out for play time
Do you have a specific size requirement or budget? If we know that, we can offer some realistic suggestions too for you, that way we don't suggest $1,500 birds haha