If your regular "tow ground" is a #12 wire,you will be OK. On the other hand,a separate #12 ground would not hurt.
I am doing the same with just the regular ground and it has been working well for many years on 3 diffrent MH.
PS. Everyone is entitled to my opinion!
Siggy & Ursula
2011 Dutch Star 4020,ISL 400,Compr.brake,FTL XCR,IFS
2015 Jeep Cherokee,4x4 Active Drive II,V6 , Brake Buddy,Roadmaster Sterling,
Camping since 1975 Pop-Up,1986 22Ft.TT,1999 Gas MH,2005 KSDP,
2011 DSDP,FMCA 368283
I already have a ground run from the MH to the Toad for the tail/stop/turn lights and it also works for the "Charge" wire. I use two 20 amp circuit breakers, one at each end near each battery. Has worked flawlessly for over 7 years. I would not depend on using the hitch/towbar for a ground connection, more positive to run a ground wire.
2004 Southwind 32VS 8.1 Workhorse chassis
2002 CRV Toad
U. S. Gear Unified brake system
Retired Fire Captain, SFD