Speaking as an instructor, I not only like but require parents to be involved in their kids training. Silently and with their hands in their pockets
. It is nothing personal but the fact is that she is training and you hired an instructor to train her. I am guessing because if you could you would but if you are not an instructor it is not a good idea. When it comes to family I prefer to allow someone else I trust to train them.
It keeps the parent/child, husband/wife dynamic out of the picture. I tried teaching first wife golf and how to ski - stupidest thing I did in that marriage. Tried to help second one with algebra - even dumber. I let my OW instructor cert my son and I didn't even go on the dives the second day of checkouts.
I'm sure you are a great dad. But I'm also betting that like me and others you want her to do well. On her own. Helping her with gear setup, studies, etc is really not helping her. This is something she needs to be completely responsible for and learn herself. If she were in my class you would have to be at every session - pool and classroom. You would not be permitted to interfere in any way with the class. If you did her training would stop or her mom would have to accompany her or even a grandparent. You would be involved in the sense that you would know what homework is required and I would expect you to encourage her to do it. But not do it for her as I would know very quickly if she did not understand something.
In the pool you could observe and even be her buddy for things like air shares and no mask swims. Unless she is physically unable to do something you would not carry her tank, set up her gear, or carry her weights even. I might even have her set up your gear just for the extra practice. You could do the predive buddy check with her but she would lead it.
You have the opportunity to get a dive buddy who will be there for a long time and share something really special. Don't screw it up by jumping in and even giving her a hint that she needs you to do something.
Finally back to the dynamics of family - as an instructor I can require a student to perform to a level that you cannot. Because she's your daughter you may even subconsciously allow her some slack. That could be very dangerous. She can get mad at me for making her do a mask clear 4 times or repeat the reg recovery and it is no big deal. By the next class she'll be over it. But if she gets mad at you she has to look at your mug for a week or whatever and there will always be that tension that doesn't need to be there. So let the instructor do his/her job. Later you can give tips you have learned but don't be suprised if she blows you off at first. She may discover her own way that works better than yours. I've seen kids surpass their parents skills very quickly given the chance to. I've also seen parents hold their kids back by insisting that they only dive with them and dive the way they do. There was one dad who probably ruined his son's diving. As a DM I helped with this kids OW and by the end of the third dive he was doing a decent frog kick, trying to stay in trim, and was someone I'd dive with in a heartbeat. And he wanted to dive locally. But his butthole of a dad insisted he only dive with him on vacation in clear water because there was nothing to see. Whined about 30 ft vis on the Duane. He was a trainwreck and had no desire to improve. The way he was diving was good enough for him. I wanted to smack him.
Don't ruin her enjoyment of the sport by sticking your nose in too early and too often. Just dive with her and she may show you a thing or two!