My girl is almost 3 and she loves to have mom brush her teeth (most of the time) because I put her on my lap and then she lays in my arms. I chat with her and tell her things while she gets brushed.
For the last few months she brushes first, then mom gets a turn and she loves the extra cuddle time. and BTW, we started out standing & holding her head, but I found this was much more gentle on both of us. On her finicky nights I let here play for a while and say "let me know when you're ready" and it doesn't take more than a few minutes of playing for her to let me know she wants mom to brush.
We also initially started saying "we have to get the bugs (or dirt) out", and she doesn't want bugs in her teeth. That line compels her to make sure she gets her teeth brushed every night. You can take the bug story a lot of places to get the message to her. good luck!