Me too, even as a relative newbie.

) After seeing Henry's breeder's herd and how enthusiastic he was about chins, I definitely 'caught the chin bug' as he put it. Going to shows and reading results in the NCS Gazette, I've been quite sad to see that attendance isn't really that high, and it's really the same names that come up each time, there don't seem to be as many breeders of chins as I would have expected. Probably only a certain number would be sustainable in terms of finding homes etc., but there does probably need to be new people, I just recently heard that one breeder I know may be giving up, and she was one of the (like me) younger in the hobby too.
So, and I hope woman in shoe understands this, the last thing I'd want to do is discourage someone who is after all in the same position as me, just wanted to share some of the basic information I do currently know, to try to help out, just as people have and are teaching me.
It seems those who didn't start out with a good pair now regret it, so it's something beginners like us can only learn from. Breeding so children could experience it would definitely not be a good idea, as as you've seen, things can go wrong. I know myself how heartbreaking it is to lose an animal when breeding, as I lost my lovely Campbell's russian hamster female when I was a child (10). We hadn't intended to breed, she became pregnant due to being missexed by the petshop, but my mum had actually bred hamsters before as a young adult, we learnt as much as we could, I read every hamster book I could get my hands on over and over, especially the ones on dwarf hamsters, I waited every day excitedly till we'd have babies arrive. She still died, on about the night, or close, she would have been due (a sudden heart attack, may or may not have been related to her pregnancy, she was quite young so it may perhaps have put too much extra strain on her), I came down happily to check on her and see if she'd had babies only for my mum to have to tell me she'd died. I think there was probably nothing we could have done but I still felt in many ways responsible, and so sad at the loss of both her and her babies, still think about her.
I say this since you mention the interest and involvement of your daughter, and since you do know from your past experience things can go wrong, you're in the ideal position to and I'm sure will explain this to her and make sure she fully understands before you begin breeding chins.
I don't yet breed but would like to, I would love to be able to show chins I'd bred myself, and hopefully do Ok with them. I love velvets (would focus on velvets and standards), and would like to aim for chins that are show quality, hopefully very blue as is my standard male, one of his best qualities though he is on the small side, but preferably less extremely brevi than the velvets that are generally seen, still blocky as is required but with a more moderate head shape, as that is what I prefer. Right now I do not know enough, I need to learn more.
I don't know whether shows in the US have an assessment class, as ours do? If so, it'd be possible for the TC to take Gracie and Hayley, and if she doesn't want to compete yet, still get an evaluation of their qualities from a judge, which can be very helpful.
And now after having typed all that I've just had to go and chase my standard boy to retrieve a sock. Chins, eh?