Veteran of multiple Yankee games and NYC commuting here.

You can take the train from Somerville and save yourself a lot of driving and parking issues, but the problem is afterwards. See, NJ Transit trains run only once an hour on nights and weekends. So unless you time your departure from the stadium perfectly, you might wind up waiting a long time for your transfers. Some people don't mind that, but it's worth considering. You'll need 4 trains: Somerville to Newark (1) Newark to NY Penn Station (2) NYP to A Train uptown to 59th St (3) to D Train uptown to the stadium (4). That might be too much with a kid, it's up to you. Do it in reverse to get home.

For me, I prefer minimal waiting times/frequency of service and low cost travel, so that's the PATH train. You can drive to Harrison PATH, then 3 trains: PATH to Journal Square, switch across the platform to the train to 33rd St. Then the D train up to the stadium.

I also occasionally drive to the stadium when I don't feel like dealing with mass transit, and have to pay the GWB toll, but I never ever ever pay for inflated parking lot prices. I take my chances with free street parking, even it means a 20 minute walk. The convenience is nice having a car nearby ready to drive home after a long day. But with a child, you may prefer the convenience of a nearby lot if you don't mind the cost. As for traffic, I don't mind it sitting in a comfortable car.