I'm in UB the third week now, and I can walk half an hour across the city in the middle of the night without any problems. I consider the city safe. I don't think you will leave your kids outside at night, so I don't see any problems.
You should only have a very good eye on your children, when you are near streets, roads, anywhere where cars drive along. People here drive like hell and much too fast, so be very careful near streets and especially when you cross streets. Generally I wouldn't say that UB is a city for children, but for some days it might be quite interesting for them as well.
Have fun in UB