Other posters already asked what your hubby would be happier doing. If he is torn, then maybe there are a couple question you could ask yourselves....
First of all, I also agree that you can't count on the bonus!!! My hubby has been promised bonuses for years and has yet to get what he was told he'd get. Or ANYTHING, for that matter.
If you can afford to have another baby, will it affect the newborn stage, him being gone some nights?? I know that it's hard to take that on by yourself if he's gone and you need a break!
Do you have family to help? It would probably matter a little less if your husband had to work more, if you had a mother/MIL around to help out.
The nights that the restaurant says hubby will have to work??? Is that a pretty safe estimate, or is that just what they say to get him to come back? I know I sound cynical, but my hubby has worked for corporate America for many years, and soooo many times, what's told to him in a job interview or in a new position, is NOT what ends up happening. If you guys trust what is being said regarding the proposed hours, that's good.
I don't know how old your kids are, but I'm assuming the oldest isn't in school, yet. A lot can happen in 5 years, but I can tell you that the older they get, the busier it gets. It's a different busy than the diaper changes, potty training, playdates, etc You get into the sports, music lessons, birthday parties, etc. and you need extra hands!! ( to drive the chauffer's car!!!) It's just something to think about.
How important is the private school? It's obviously important enough, or you wouldn't have mentioned it. Is your district not a good one for public schools? I didn't have a whole lot of confidence in our school district when we moved here - but, it was supposed to be temporary and we figured it would be ok for a year or two. Well, 5 years later (after our original plans fell through), we are in this school for the long haul and it's turned out to be a great school district! There would be no harm in starting your oldest in the public school, then transferring him out if it's not good. If you already know that the ditsrict is really bad, then I understand the private school desire.
I wish I could say one way or another, that's what we'd do. I don't know.. But, maybe they'll be some feedback on this site that will help! Good luck either way!!!