Is the plumbing in the 1967
AS original, and maybe copper? Tapping into a hot water line in the trailer -- to "back feed" the rest of the hot piping -- is OK, as long as there are no OEM check valves in the system. [*] There may be one as the trailer's hot water leaves the water heater? Or where the cold water enters the water heater? You have to know the details here. You don't want your "new" hot water going back into the water heater, and warming up the cold piping, and maybe back-feeding through the pump into the water tank [if the check valve there is bad or leaks].
You should probably consider adding check valves, per above questions, to keep you household hot water going where you want it to go.
Will you also have city water hooked up to your trailer to supply cold, and maybe to supply the water heater? Check valves all over will isolate your intended uses IMO.
If you provide more details of the existing setup, you will get better advice IMO.
Good luck, Billy.
[*] PS -- on edit -- any OEM check valves should only work in one direction of water flow, but the entire "check valve" part of the equation must be considered IMO.