grab your multimeter & check the outlet voltages. If you don't have a MM buy one soon as it will be your best friend RV tool. Also grab a 110v continuity tester. They plug into each receptacle and report back any wiring faults.
While not likely simply replacing house batteries will cause this issue, it's kind of amazing how RV wiring issues seem to sense just when it's right to cause maximum confusion.
Do your other AC receptacles work and show 120v? Remember they are all wired in series so if one in that circuit has an issue another, several or all on that circuit can fail or provide low voltage.
Electrical, well 120v, is pure black magic to me so just sharing things I've stumbled into.