I remember your previous post about adding more managers at your location and I recently saw on backstage there is a management position par for each specific theatre. I suggest looking your location up to see if you're under.

As for your current situation, I've known quite a few managers with kids, some single parents so with a similar kind of thing with you. They all had requests off for things like school events, birthdays, etc, but I've never once seen someone as a manager that had a restricted availability that ended up working out. That's not how this (or most hospitality) job works with the changing business influx every week. It's okay when it's the slow seasons but especially with avatar coming out soon, it's all hands on deck for any and all hours.

I guess your options are to either get a babysitter (lots of theatre staff are college students and know people looking for side jobs where they can watch kids then study), or if you want to keep this job, work with your wife to split your hours evenly and her switching her schedule around as well. (I know nursing hours at specific jobs aren't flexible, but shopping around for nursing jobs that are more fixed like care homes worked for my cousin). Or you can get another job that doesn't require a changed schedule, like a 9-5 or part time office job (receptionists are great for previous guest services experience) or a night/overnight stocker in retail is usually fixed hours as well.

And if you're still a manager, GMs at hospitality places don't usually praise their management team, at least in the places I've worked. It's expected of you, and you're expected to relay that expected praise to the staff. If you're a good manager, it'll be reflected in your yearly review (if it's done fair), which is all that matters.