A group of us ate at U MODRÉ KACHNIČKY back in October. We have an annual tradition of going away somewhere in Europe for a long foodie weekend and this year was Prague. This was one of the restaurants we ate at. We opted for the 7 course House Tasting Menu and for the most part was very good, some excellent wine pairings. It wasn't particularly busy when we went (a Saturday night) and we were the penultimate table to leave at 11:30. It's old fashoned, a bit musty, kitschy and tired and although it has several rooms it all feels a bit cramped. Not knowing the children I couldn't say whether or not they'd enjoy the food, it's quite traditional, lots of game, duck and offal although I suspect they'd enjoy the dumplings.
We also had a very good lunch at Lokal, www.lokal-dlouha.ambi.cz/en/, it looks a bit austere but that's part of its charm. They brew their own excellent beer on site. Expect it to be busy but service is good. The children will probably like it plus they offer chicken schnitzel and what child doesn't like schnitzel? I can recommend the pork shoulder and the house sausages, I can't advise you on the bull testicles with mushrooms as no-one in the group fancied them on that day. I probably wouldn't consider it for a New Years Eve dinner but certainly would for lunch on New Years Day.