Normally I am a huge proponent of DIY, but 3200 miles and 2 kids...this is where the trusted mechanic(is there such a thing?) and $100 bucks would come in handy. That would be for a thorough inspection. Or, here's a better tact, take it to a repair shop, tell them you are going on a long trip and you want to see if it needs anything. Guarantee they will find everything and anything that is wrong, going wrong, or is thinking about going wrong.
Funny story, my buddy did that with the local shop a few years ago when he was going on a 1000 mile trip in a 10 yr old hand me down Ford with 200K miles on it. I laughed and said this will be good, $4500 in repair quotes later, I advised him to fix the back brakes for $200 bucks and be done with it. Car wasn't even worth $800.
Yup, if you seek, they will find it.