x2 that April is too early for Yellowstone. Roads are literally closed to vehicles - other than snowcoaches - in April, the exception being between Gardiner and Cooke City MT, near the northern edge of the park. Plowing the many-feet-deep, packed-down snow takes weeks to finish. There are no hookups in Mammoth CG, so you will not be able to run your furnace and your water pipes in the camper will be at risk of freezing up. You may look into CGs in Gardiner, just outside the park; if they are open, you would have access to hookups and can drive into the northern part of the park from there. You will not be able to drive to the rest of the park (i.e. Old Faithful, the falls at Canyon, Lake area, etc.) at that time of year.
That said, you may want to do some research about specific parks in the other areas you plan to stay. Many state parks in the northern tier - as you know, being from Ohio - may be closed that early in the season as well, or will offer fewer services (i.e. no water, etc.) Flexibility will definitely be required as you travel. Those that are open, however, will probably have very few campers in them, and should be nice & quiet!
