Have you shown her photos of kids who have had braces taken off and haven’t cleaned them properly? That was enough to scare my two into brushing properly!!
The orthodontist told them that if they didn’t brush properly they’d ruin the enamel, showed them photos of what that looks like, and said that wasn’t fixable, so they’ve both been very disciplined at brushing for 4 minutes each time and using the tiny brush to get in between the brackets.
DD (12) has also taken responsibility for cleaning her blocks twice a week without any prompting, which is lucky as I know I’d forget, (but she’s the one wearing them all day so she has a constant reminder!)
By the time they’re old enough for braces they really should be responsible enough to care for them (barring any SN of course) so this isn’t on you to feel guilty, your DD is old enough to take responsibility for her own oral hygiene.
Get her a timer, a good mirror in the light/by the window and some disclosing tablets (mine were given all of those as part of their first appointment, so if your DD wasn't it might be worth talking to the orthodontist about offering this - it did cost, like £10-15 I think, but had everything they need in a little pencil case )
And make sure she has an electric toothbrush (Superdrug own brand one gets very good reviews and is much cheaper than other makes) and one of the little pointy toothbrushes for getting behind the braces. Having the right tools for the job will help.