Hi Mr. Mark are you sure you don't mean 70 miles? We did exactly what you are suggesting it's been a few years back but I don't remember the two being quite that close.
Technically, 7 miles is pretty accurate. The northern boundary of GTNP and the southern boundary of YNP are separated by several miles of national forest land and the roadway there is called the John D. Rockefeller Memorial Parkway. The road between the 2 parks reopened yesterday; I would doubt it will close again, unless a new fire breaks out.
IMO, Colter Bay is BY FAR the best full-hookups CG for the Tetons. There may be some people who have cancelled plans to travel there because of the fires, even well into September, so the OP may have a chance - but act now! Grizzly is very nice, but it's a long day trip from there to Jackson and back. If you really want to spend some time & enjoy the Tetons, stay in GTNP if at all possible.