You on the bus, train or car?
There's a few nearby but might not tick all the boxes.
There's the glover's arms - more of a restaurant but has a small outside bit and area for just drinks. No football though. Not sure on their kids rules if no food? They may also not be very welcoming to football fans after the behaviour of Motherwell fans in there at end of last season. Vandalism etc
Theres the Tulloch a bit dingy and old, football on via a dodgy box kinda place. I think they'll be fine with letting kids in though. Hearts had a supporters bus last season, good chance Hibs may also this weekend!
The Muirton Suite at the ground has the football on. Officially it's no away fans, so will depend if they've got someone on the door or not preventing away fans entering. Ayr fans were in there on Saturday past. Kids also allowed. Not the biggest space though.
Not sure if I'm actually helping at all there but might give you of an idea where to not bother going!