Look at Travelodge or Premier Inn chains. You have the option of staying in Manchester city centre itself or closer to Old Trafford at Salford Quays. There is a shopping centre, Imperial War Museum North and Lowry Museum at Salford Quays, with Manchester city centre being easily accessed by tram. Public transport after a match is bedlam and not recommended for young children, so you would be better off staying closer to the ground or going to the shopping centre after the match for some food before you attempt to travel on public transport.
Note that the date of the match can change to fit in with the TV schedules - any time between Friday night, Saturday afternoon or evening, Sunday afternoon or Monday night. The actual date and time will only be confirmed 3 weeks out. This doesn't help with trying to plan your schedule!