|Your puppy should not be sleeping with your daughter. You didn't say how old your daughter is, but in any case puppy should not sleep anywhere but in its own bed until it is reliably potty-trained (at least 6 months old).
Dogs have a natural aversion to soiling where they sleep, but to a chihuahua the other end of the bed is the other end of the house to you or me.
Puppy should be introduced to crate training. It will not affect bonding at all, you and your daughter are higher ranking members of his pack, sleeping with you is a privilege he has to earn, and he will understand that.
I didn't use a crate, I used my bathroom since it had a tile floor and a litter box. Other than that, not much difference. He should have his own bed, with something soft to lie on and something soft to curl up under. A cuddly toy is also good, just make sure to remove button eyes and etc. The crate should be small enough that he really can't run around too much, you can get a temporary piece that will divide the crate and let you expand the space as he grows. He should be able to stand up, turn around and move a few steps but no more than that. Don't put food or water in with him.
Give him a chance to eliminate, put him in his crate and tell him "Goodnight, go sleepy now". The first few nights might be hard, as he will possibly cry as if his heart is breaking. Don't reward him by talking to him or going to get him, it is like teaching a human infant to sleep in its own crib. He will get used to it, but it will be harder since he has been accustomed to sleeping with your daughter. It may help if he has something your daughter has worn to sleep with, so it has her scent which should comfort him.
He should be given the chance to eliminate as soon as he's taken out of his crate, fed and watered, and given another chance to eliminate before going back into his crate.
He should be in his crate whenever it isn't possible for someone to watch him. Never use the crate as punishment, he should see it as his den, his place to be when he wants to sleep. When humans are home, he should be with them and not in his crate. It's not his home, it's his bedroom, leaving him in it when his humans are home and active is cruel.
Give him much praise whenever he 'goes' where he's supposed to, ignore it when he has an accident unless you catch him in the act, in which case tell him "NO", take him to where he should go and tell him "Go Potty, good boy". I've been told that boys are harder to train than girls, I have two females who were pretty easy.
Your chi may not mind using the same litter tray as the cats, as long as your cats don't mind it's not a problem. I have found that my alpha female likes her litter tray cleaned daily, more than three pee pee clumps and she'll look at me as if to say "You want me to go in there, it's Dirty!" Once I remove the offending clumps, she's happy to hop right in and do her business. My beta female couldn't care less if I ever clean hers. Your experience may vary. The reason I have two is that my little princess refuses to share with her lower-ranked sister. Since I got them at different times, she was already trained and had run of the house before her sister arrived, so two trays were necessary.
A good source of information is the book Chihuahuas for Dummies.