You will have no problem getting a site in Mammoth, because April is too early to be at Yellowstone. The first roads that open in Yellowstone do not open until April 17th. Many of the roads do not open until the first half of May, and some not until May 22nd. Be aware that is only the roads opening, not the related services. I doubt there will be any place to get water or dump tanks, the campgrounds with those facilities do not open until later. You can expect temps to be below freezing nightly in April. Personally, I would re-arrange my trip to do Yellowstone at a more benign time.
