Hamsters make shitty pets. They bite, they wake up up in the middle of the night and generally don't like being handled.
I've had both rats and hamsters and would, in a heart beat, have rats again.
They are very very clever creatures and will show love in the cutest ways. One of mine would hold onto a finger and lick it and go to sleep or round my neck (and in my cleavage!). Mine could be recalled like a dog (they ran from the floor, up my leg and onto my shoulders) and played fetch and I trained all mine to go in the corner of their cage to wee and poo.
Agree with others they need a nice big cage (with several levels and lots of toys/ ropes/ hammocks) and need interaction for at least an hour a day. They enjoy human company and can get stressed if their main handler suddenly doesn't play with them anymore. You can let them out their cages and can be trained very quickly with food as a recall (I would whistle for mine to come to me) Mine also like to climb up the dog (long haired German shepherd) and sit on her back and ride around the house.
Check out youtube for videos of ppl who have trained their rats, some are amazing. There are also loads of sensible advice on youtube as well.
Do you have a local rat fancier near by or pet store that might let your kids handle them? I have a garden centre with a pet area which allows this under supervision.
Are you freaked out by rats because of their tail? If so don't be. My father was a pest control officer and hated rats but even he came round to my 1st set of pet rats and even bought them treats and made them little cabins from wood for them (the 1st being at xmas)
Cats should not be an issue (or dogs!) if they have been around smaller pets before. My last two were in a house with 5 cats, the only issue I had was one of the cats liked to sleep on top of their cage and would wake up finding their tail being cleaned by the little critters.
I had a plastic carry box for trips to the vets. Regarding holidays, they would just need someone to feed them and change their water, I assume whoever looks after your cat can do this. They don't even have to make contact with the rats (though they will come and have a nose around) at new people. Just make sure they wash their hands before and after feeding them (as any normal person should when handling small furry things)