Yes, a rat WOULD be up for some portion of the day. Though they are naturally nocturnal you should get at minimum a few solid hours throughout the day where they will LOVE being handled and given treats and such. Some people have had success with training their rats to be up in the daytime and sleep in the nighttime, but I kind of think this is somewhat unhealthy for their rythym. It would be kind of like us working backshift - can screw us up right?

Again, a lab would work well. I think that Sky or Sept has a lab (maybe? I am not sure) and is in a wheelchair too. She does manage to walk her dog ok But again the dog would have to be trained too.

Maybe you could look into getting a dog that is trained to be a companion/service animal AND is good with kids?

Siamese cats are pretty neat. They are quite playful for sure. They are also VERY vocal in most cases, so be prepared for at least some meowing. And again, I would go with a kitten for sure, that way they grow with the BOYS (sorry about that, why did i think you had twin girls? Dont mind me, Im just riddled with pain today and kind of foggy from the meds)and will get used to being picked up and hauled around, and tails pulled ect.

Bear in mind that even with an animal that is well trained or gentle, it is still imperative to teach your children to always be gentle and respectful of a pet. Even with three month olds, they will respond to tone of voice and will watch to see what you do and copy that.

oh and about the cats who dont respond well to being picked up - nine times out of ten this is because the cat was never completely or properly socialized, or that it had a traumatic experience somewhere in its past. This is another reason for getting a kitten in this instance. And if you decide to do that I can provide TONS of information on how to safely socialize a cat. ( I have had .. lets see.. too many cats to count in my life :P)