Here's one approach. You might suggest that they can have a couple of short, planned meetups with you during the trip. Depending on your family's dynamics, that might be an easier sell than just refusing their participation. Something to the effect of "hey--why don't you guys meet me in Yellowstone and we can spend a week there together."
Sure, they're worried about your safety, etc., but they also very likely just want to be involved in some way because of how exciting this thing you're planning is. That's something I found about my family during my coast-to-coast trip last summer.