What works well with varying frame rates

i want to edit my footage instead of being pretty damn dull

what im currently using is davici resolve to edit and my frame rate isnt the most stable meaning that it will go out of sync with the video with cuts in audio and video
(they are recorded with relive so they are the same track so without separating them then back together adding a other step i dont really want to do)
my current fix is to go back to using bandicam or i could do 30fps recording

my main question is that is there any good editing software that supports variable frame rates stopping it drifting out of sync