I think that this should be taken as an opportunity to evaluate your household.
When my SD wanted to live with her mom, we sat down and considered various data. For example, she was doing well here in school, and socially, etc. The main reason she wanted to move was to see her mom more, so for us, the response was if BM wanted to go to court, she could, but we would rather she just take the visitation she was originally offered. Her mom is an "out of sight, out of mind" person so there wasn't any reason to move SD other than she thought she'd have more of her mom's time. Her mom works weird hours, so that really wasn't an option. DH considered the school SD would attend, the activities she would be in, the supervision she would have been under. He talked to SD pretty frankly about how he saw it (without bashing her mom). It came up again when BM divorced and SD wanted to keep her company but that was even worse. She didn't have a fixed address. Another conversation, and the matter dropped for good.
It may also be that the honeymoon is over and your daughter thinks the grass looks greener. Do you set up the rules or does he? Or do you present them jointly?
I suspect that there's a little of everything going on. She's had some BIG changes in the last couple of years and probably feels like she lost you in the process. Eight is like a mini adolescence. If she's moody, that can contribute.
You admit that you aren't always there when she needs help, she doesn't get a lot of mom time and she's struggling in school. I realize that in this economy most any job is one to keep, but maybe it's time to evaluate how much you work and the hours. Would it be better if you went in earlier and got home for dinner? Could you maybe bring work home to do after she's in bed? Can you work an alternative work schedule so that you work a little later for 9 days and are off on the 10th? What about weekends? Can you carve out time to go over her week, spend some time, etc.?
The other part is, what's it like at Dad's? Would there still be chores and homework? Something my SD did not consider is that life is different when you are somewhere every other weekend vs all week.
While I wouldn't just say, "Okay, here you go", I would sit down and really consider both sides. Friend's grandson moved with his dad in middle school and while it was HARD, for them, it was also right. The kid graduated HS with honors when he'd been failing before. He still spent all summers, every other holiday and other various breaks with his mom. Do hammer out a solution that keeps her in one school for the year. No getting to Dad's and in November saying she doesn't like it there, either.
I do think that it is good that he brought this up to you now. When SD was little, she was telling her friends good-bye, but BM had not spoken a word to DH. Just made SD promises we had to clean up. Much better to be in the open, however painful.
Hang in there.