I don't think it's ideal to start without him but I think that as long as you explain the circumstances (babysitter, long drive, etc) to them and make it clear that you're sticking to your 7 pm reservations, then it's up to them if they are ok with that or not.
Ideally the original conversation would have included that info so that when sis said that bil couldn't make it till 8 and that y'all could just hang at the bar till then, you might have replied with those answers on the spot.
Since you and she are close, though, she should understand, once you explain your reasons, and then either (as PPs said) just decline the invitation or agree to your timing. I also agree with PPs that once BIL does arrive, it's going to defeat the purpose if he then begins his evening at 8, beginning at the exact same spot you three began at 7. So, ordering apps, then main dish, then dessert, while the three of you sit waiting... well, you may as well have waited for him in the first place.
Maybe he can check the online menu in advance and pick what he wants and call ahead when he's on the way, and sis can order his dish so it is served just as he arrives? It would still cause some delay but not as much as him arriving, perusing the menu, etc. We have done this before when someone was running late. Usually the server can let you know how much lead time you need to give the kitchen, and bil can call when he's that much time away from arriving.