Did you take her to the doctor about the nail biting?
It might be an anxiety thing or a compulsive thing or in extreme cases even a self harm thing.
I'm not at all sure that acrylic nails is the answer to the problem.
If it's a compulsion she'll find something else to pick at.
You and your ex will be co-parenting your daughter till she's 18.
The teen years can be a rough ride.
Is this really a hill worth dying on?
It would be worth it for you and your ex to get some counseling so you can talk about these things with out accusing anyone of anything and come to agreements.
I couldn't wear makeup till I turned 16.
No not everyone her age is wearing it - and many who do look ridiculous.
Last year in high school the thing going around was 'kitty cat eyes' - it was pretty silly.
Additional:
Jill K - Interesting but I've never heard that "acrylic nails can be beneficial to already damaged natural nails".
I've Googled it and all I can find - even from dermatologist sites - is nothing but how damaging acrylic is to natural nails, nail beds, increases chance of fungus, infection, etc.
If you have a source I'd love to see it.
It can take months for nail damage to grow out.
I bruised my thumb nail working in a kitchen in May (little dark spot that started at the moon and slowly advanced toward the thumb tip) and just NOW (late Sept) it has finally grown out to where it's gone.