It might come up without cutting it just grab and pull. I've been able to use that method of two different RV's and it works fairly well. If it is a real bear to pull up I would just caulk over it. I have used and like Eternabond, but I've never wrapped it around an edge like where you have the cracking.
As far as the big puddle of caulk in the back corner, I would definitely caulk over. It looks like there is a low point there and the manufacturer filled the area with caulk to prevent a standing water puddle that would be more prone to leak.
