One piece stem/handle?

Recently, our tub faucet has started leaking from behind the hot water handle when it's turned on. From what I can tell, the stem and handle are one piece, because I can't get the handle off. If I keep turning the hanlde towards the left, the entire thing, stem and all, comes out. Is this a true one piece or is it just that frozen? I have replaced the washer at the base of the stem, still leaks.
ETA: This is a mobile home from the 70's. Entire place rebuilt to a frame home in the 90's, but interior stuff is still from the MH.

Get yourself a handle puller available from any supply house and most home centers. Often the handle becomes stuck tight after years of use and can be a booger to get off. The handle puller makes it alot easier.

Good luck