In normal times, I'd suggest the train with an advanced purchase ticket. However... right now you've got all the strikes around pay (any one of drivers, guards or signallers could wreck it), plus you'll mostly be travelling on Avanti who are being especially terrible. If you were going up the day before the train might still work, but right now on that route I wouldn't risk it on the day before a flight

If you can easily get into the centre of Birmingham to get to the coach station, National Express wouldn't be too bad. It'll hit the same traffic you would, but at least you can entertain your kid instead of dealing with a meltdown when trying to drive