No way to tell over the internet of course, but it all sounds within reason. The wobbly brakes presumably were warped rotors, which they resurfaced. Many shops wouldn’t resurface warped rotors, they’d just replace them. But it may be the way your hub works, replacing the rotors, the parts cost is expensive so resurfacing worked out better. The most common causes rotors warp are b/c they overheated at one time or another during heavy sustained braking, or b/c the wheels were installed on the hub incorrectly. If one rotor is warped and the other (on the same axle) isn’t, then that bears more investigation. But if both were equally warped, and they installed the wheels on the hub correctly, I’d say you are good to go.
Most batteries leak a little at the posts, often showing up at corrosion on the post and the post connector. If you have battery fluid dripping down the side of the battery and landing at parts below the battery, that has to be dealt with now; but if it is just the typical post/connector corrosion, cleaning that up, maybe replacing the connector, good enough. Making sure the battery and alternator voltages are correct with and without the engine running would make sense too.
The bumping sound after putting the vehicle on the lift is a little unusual, but it could happen. When the car has been lifted by the chassis, the wheels are hanging freely, and that temporarily changes the geometry of the suspension components to each other, since there is no weight on the wheels. The suspension interfaces live inside rubber bushing and it might take a little driving for it all to come back into the same geometry the way it was before. Suggest to make sure that problem goes away after a few drives, before beginning your family trip.
For a long trip like that, it’s a good idea to visually inspect all your tires, including the spare, making sure they have enough tread and nothing unusual is happening, like cracks in the sidewall, bulges, or unusual wear patterns. Next make sure they are all inflated to spec, including the spare. If you’ve never used the tire jack, get it out and make sure you can change the tire in your driveway using it. That’s not something you want to learn with a flat tire on the side of highway 1. I always bring along a small tool kit and socket & ratchet set on a trip like that, sometimes it comes in handy. I had to do an emergency fix a broken seat belt retractor on my VW Rabbit one time for example.