Colorado in June will be a nice time to visit, although it can still dip into the low 30’s and high 20’s even at that time of the year. Even though the snow should be over by then (though we here hope not

) …one website that I always recommend is
CoTrip.org . While snow will not be the concern, CDOT is always resurfacing areas of I-70… you may want to check it as your travel time nears. Both bores of the Eisenhower Tunnel were resurfaced last summer, but the approaches are in need of some serious repair; it may happen during your slated time.
You state you: "…are planning to stay at Sam's town rv park…" This must be in LV as I am not familiar with that name here. There is an RV park between Frisco & Breck called "Tiger Run" that would probably fit your TT and there are some State Parks around Lake Dillon ... I could recommend some great boondocking spots (but yer TT might not have enough ground clearance :-laf )
As far as mountain travel west of Denver…: do you have an exhaust brake? If not I would recommend taking the interstate at no more than the posted speed limit. Mountain curves can sneak up at you if you do not pay attention to signs. And it will probably be the steepest decents (sp?) that you may ever encounter. If you are not familiar with the road, I highly recommend driving it during the daylight hours. It is quite dark at night, but traffic is much less. Keep in mind that weekend travel (into the hills on a Friday evening westbound... and Sunday eastbound back to metro Denver) can be very heavy on the I-70 corridor. Many Denver folks head into the hills for the weekend and traffic (especially during holiday weekends) can be very heavy!
West bound I-70 after Vail is reletivly less steep and it is a nice drive all the way to the Utah border. But, again pay attention to the posted speeds, especially in Glenwood Canyon!
Feel free to ask any questions. I will try to help you as much as possible.
-frank.