Thanks for the info-- we are not trying to get the hose out, but trying to get inside the entire faucet assembly to fix the leak at the "T" between the hot and cold water pipes. DH looked, but we do not have an exterior access panel.
That's probably corrected on the newer units. DH just wanted to remove the cover over the plumbing for the faucet so he could access the leaking area. We live in the boonies in Southeast Colorado and are not close to any RV store to get a replacement faucet assembly, so we have to just fix the leak so we can leave in a couple days cross state to camp. So, after removing the hot and cold handles, DH did "dremel" out the back of the hole in the top part of the plastic face covering the faucet plumbing to remove it from the top pipe that the hose affixes to. This revealed the problem area, which he then sealed with Loctite. After testing it, he put the face back on the faucet, reattached the handles, and will caulk the whole thing in place. Whew. Hope it works! You're right, we do have lot of life in our TM!!! Need a working bathroom, for sure. This winter we will winterize carefully.