What type of RV do you have?
Generally, no, the Furnace exhaust vent is not the same as your hot water vent.
You need to locate where your furnace ignation is - since your hot water works fine, purging the LP lines will most likely do no good (although check, can you light a burner on your stove? if so, then your lines are purged)
I agree with others, I am betting something is clogging the igniter in your furnace (and it could well be critters!...they LOVE LP fumes!)
Your blower is working so your vents are not blocked, you have hot water and can light your stove, so your LP lines are working. Last culprit in the chain is something malfuncting with lighting the burner in your furnace.
(Oh, and check your furnace vent as well to make sure you do not have any "squatters" in there as well