I've also got kids (6, 8) who are learning to run with me. I use a "learn to run 10k" program, but I have no intention of finishing it and I think just a few km is enough. We don't have any goal in mind, no PBs, just getting to a higher fitness level where they can run continuously for a short time. The kids at the school recently did a charity run, and only 10% of the kids could "run" more than 500 m without stopping and gasping for breath. The kids recently did a run/walk of 5 km for charity. Many adults could not even do that. But I digress.

I would suggest going for a run right BEFORE dinner. That is when we do it. Don't take any water either, unless you're going for a run over an hour in duration. Otherwise, you're asking for trouble. I don't know of any athletes who eat dinner then an hour later, go for a hard run. For myself, I cannot run on a full stomach at any speed without getting a stitch if I have eaten a meal within the previous 3-4 hours.

Even better, do your run first thing in the morning before you eat breakfast. You would have enough glycogen stores to do a good run at that time, without having to eat anything. You'd have to put her to bed earlier, but if it works better for you than before dinner, that's the way it is for you.