So perhaps you'd be able to shave off a buck or two an hour, but that's only going to save you $10 at most, so lets look at the rest of your math:
It obviously depends on what part of town/the country you're in (a decent burger in Manhattan costs $20, for example), but $50-$100 is a lot of money to spend on dinner for two when you have a young kid and are tight on money. There are less expensive, hole-in-the wall type restaurants all over the place that have surprisingly good food and are cheap. It just takes some time to find them.
Another option, if you are looking to go out with friends, is to start a rotating dinner club. Making a meal for 6 or 8 is only marginally more stressful than cooking for two, and by rotating around a group, you're only cooking a small fraction of the time. You can still leave the baby with a sitter so you can relax, without running up such a bill. Each time you cook, it will likely only cost you $50 (or less), so you end up bringing down the overall cost of going out by 3/4.
Also, there are many cheaper alternatives to going out to a movie. If you get weekends off, go enjoy something outside for free, and make the dinner the end cap to your evening. Or, if you really want to see a movie, spring for DVDs/Netflix instead of a theater. You're not being social during the movie anyway, and it's not as if you're likely to run into lots of people there. There's more than enough good movies out there that you haven't seen yet.
I understand that these options are not for everyone, particularly if you're used to a particular kind of lifestyle, but they are an option that will make your social life a lot cheaper.