Phoenix to Maryland

When we leave Chandler we go through Payson and Heber then on to Holbrook to I40. Then we stop after about 360 at Dancing Eagle RV Park, Interstate Exit 108, Casa Blanca NM. Nothing fancy but clean and level with hookups for $10.00 this would give you time to stop at the Petrified Forest before leaving Arizona.
Then 356 miles to Palo Duro Canyon State Park where you camp, with hookups, in the bottom of the second largest canyon in the US. Take in the outdoor show Texas along with a cowboy chuck wagon dinner at night while IN the canyon.

Grants is about an hour farther East than Gallup, but I think there may be more things of interest to do. In addition to those mentioned in the Trip Advisor link, El Morro National Monument and Acoma Sky City are not that far away.

In Amarillo, The Big Texan and Palo Duro Canyon are popular attractions.

If your primary goal in Memphis is to see Graceland, the Graceland RV Park is as convenient as you can get. It is right behind the Heart Break Hotel and a short walk to the attractions. That said it is right in the middle of a heavily developed area and Tom Sawyer may be better for the kids.

In Sevierville, there are two other parks (Riverside and Two Rivers) that like Ripplin Waters are North of the major development of the towns of Sevierville and Pigeon Forge. I would recommend staying at one of these three, if possible, to avoid towing through all the traffic. Parking in Gatlinburg is expensive and a mess. There is a trolley from the first visitor center on the North side and starting June 13 a free shuttle.

Hope you have a great trip!!!

Where are you staying in MD. With kids you might like to go a bit further on I81 and stop in natural bridge. The last part of your trip will rake the longest with the traffic so a shorter trip by about 100 miles might be easier.