RE: my dog bit my daughter...
Yes the kennel/cratemust always bea safe place. The door should be left open when the dog is not in the crate. You'll find that when they get tired they learn to go in on their own. You don't want to develope the problem of a dog hating to get in her crate, especially when she's going to use it to travel. Home goes with her.
We always leave the crate doors open when they're not in there. Our senior citizen will get in her crate when she's tired.The crates in the truck are always open as well when not occupied.
Dogs really don't get the concept of time out. They can't tell time (except when it's dinner time) or the gun cases & vest & boots & whistlesare out.
We don't have kids but we borrow them constantly to help us train our dogs. They need to know how to interact with each other. Always supervised and usually on leash or handler between dog and child.
Find a local trainer to work with you. She sounds like she could be a bit of an alpha female.