Aren't passengers with special needs supposed to notify United 48 hours in advance? It seems that this could have worked out then.
FWIW, even two year old lap children scare the heck out of me. No matter how much you love your kids, you are not immune from the laws of physics, and if an accident or even severe turbulence happens, junior becomes a projectile. Older and heavier children are that much more at risk.