My '71 bath differs some, but the only way to remove the pieces you show probably requires starting at the trim line at the back of the sink and, rivet by rivet, taking out the sink/counter piece. This does involve plumbing work at the faucet. This removal and replacement is tedious but not difficult.
Knowing the tendencies of this era of trailer, you likely have much more damage under the rear components than you have shown. Exterior water intrusion from the bumper area to the subfloor with the resulting floor/frame rot is almost universal. Taking down at least part of the rear belly pan or close inspection of the floor where it goes under the rear corner wall will usually reveal the damage. Have you checked for rear-end separation? Since you have the floor work and removal to do anyway, it's best to do it all now rather than having to dismantle or redo later.
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