We've volunteered in a national park and each camper was given the rules. One was "no tree cutting". Sure enough, the same night he pulled in (he wouldn't do it during the day when everyone could see:)), a guy was out there sawing down a 3" dia tree for kindling. He left that night along with a BIG fine to pay.
If you can't fit into your site comfortably for you then either move to another site or another campground. You don't own that tree.
Or... better yet ... definitely ask the management if you can trim a few branches. Most often they'll come and do it for you or at least give you permission to do it. This is what we do and have never been refused.
However, it's not right to just go in and start trimming on your own without asking...especially being sneaky (knowing you're doing something wrong) and doing it when no one is looking.:)