My motto generally is, "it can't hurt to ask." Maybe they need someone. Maybe you end up starting out with classes and preteam. Maybe they say no right now. You won't know unless you try. And with those costs, I'd be trying! I'd let them know your background (bring a resume, obviously), and then tell them what you've told us--it's not a package deal, you enjoying coaching compulsories, and you can't coach your daughter. Be willing to be open to what they need right now to get your foot in the door. I went to my current gym looking to teach a few classes a week--after a few weeks (and timely fill-ins for a team coach a few times), they offered for me to coach preteam and team. Not what I expected! I'm in love with this gym, the owners, the directors, the kids, and the parents--but if I hadn't given it a chance, I wouldn't be doing this! And I almost hadn't--I wasn't sure if I wanted a second job again at the time.
We also have a team coach that now exclusively coaches rec to avoid coaching her daughter. That's what works for her right now.
Good luck, and I hope you are able to find a good fit for BOTH of you.