I don't know if you need a new roof or not, it sounds to me like you do but I will leave that up to the experts.
I will say this about the caulk. The caulk is tenacious, to remove the existing caulk on my trailer would take me at least 4 hours (and possibly a lot more depending on how diligent I was in "removing all" ). Then it's about another 2 - 4 hours to replace it all. So if you figure on the low side 6 hours of work at $80.00 per hour plus materials you got your answer.
Now if I am only resealing the bad spots then it's about $150.00 worth of work. But remove and replace is a whole different ball game.