need advice for June 7-14 travel from Denver to Salt Lake City Utah

[FasTrack]

my mom, daughter, grandson and I are looking for a one way motorhome rental to drive from Denver to Salt Lake City. If we aren't able to secure a motorhome we will rent a car and stay in hotels. But we prefer the motorhome option. I have driven a motorhome in Alaska years ago and have towed a travel trailer in the Great Smoky Mountains many times so I am comfortable with the idea of driving the motorhome.
Do we need to be concerned with road conditions for this time of year? If we are able to secure a motorhome, will pull offs for sightseeing be an issue? Is it best to secure our campsites ahead of time or are there plenty of options along the way?
We are considering leaving Denver and spending the day in Estes Park area, then travel to Glenwood Springs, Grand Junction, Moab and then on to Salt Lake City for a yearly convention. We have a full week to make the trek. My grandson will be 5 months old so we want to take our time.

any advice would be greatly appreciated!