This is from one single mom who often enjoys a night out. Dating a single parent is a lot like dating someone with a professional career. We often have good boundaries, aren't clingy, and either don't mind taking things slow commitment wise or going without commitment entirely. My top four pieces of advice are -
Make plans ahead of time.
Single parents usually have a lot on their plate, and your offer of a last minute movie or night out throws a curveball. Even if the kids are old enough to not need a babysitter there are other issues to juggle. If she does need a babysitter at the last minute, offer to pitch in because short notice babysitting usually isn't cheap. That leads me to point #2 -
Offer to split any childcare fees, or show appreciation if a relative or friend is doing the babysitting for free.
That could be in the form of bringing a movie, games, or snacks for the kids. It will win points with the relative or friend, and splitting childcare will make it easier for her to afford a night out. (You don't think women is cheap for dating, do you? Have you SEEN ...