Unless the batteries are completely dead YOU DON'T NEED NEW BATTERIES. Just leave the old ones in. You are going to be on shore power 24/7. If the shore power goes out, you are no worse off than if you were in a house and the power goes off.
Once you get the MH to the place you are staying at, take a voltmeter and check the voltage while connected to shore power. It should be around 13.4V. Unplug from shore power and monitor the voltage. Assuming you don't have LED light bulbs, turn on 3-4 lights and any other 12V devices off. (You can leave the fridge on, it only pulls about 1/2 amp) After an hour or so the voltage should be around 12.6V which indicates a battery at 100% charged. After 4-6 hours it may drop to 12.4V or so. If it drops below 12V you have weak batteries, but they are not toast. If they are down to 11V they are very weak and you need to replace them at some time in the future.
You can get a volt meter at Amazon or any big box store for under $20. Some are even under $10 and would serve you well.