"Best" has several interpretations.
One best is easiest way, IMO that would be to backtrack from Red Lodge I94 then enter the park via the North entrance at Gardiner.
Another best is to enter the park by continuing on 218 to Cooke city then enter the park, this involves a lot of mountain road driving with all wonderful scenery. I think the best way to learn about that is by reading Road to Yellowstone
then making your decision.
Another best is the long route - MT191 South from I95.
All these are safe for RV's, IF the driver is comfortable with the type driving involved.
2000 Winnebago Ultimate Freedom USQ40JD
, ISC 8.3 Cummins 350, Spartan MM Chassis. USA 1SG, retired;PPA,Good Sam Life member."We the people are the rightful masters of both the Congress and the Courts - not to overthrow the Constitution but to overthrow men who pervert the Constitution. "Abraham Lincoln"