The 35K is a heavy MH and has a very small CCC. Loaded for a trip you will use up all the GVWR. So even if you upgraded the hitch (which can be done easily). The MH will be over the GCWR with anything more than a 5k lb vehicle.
Now some like mine have a high CCC. Mine is 4200 lbs. I only use around 3000lbs of that, so that leaves me with an extra 1200lbs I can add to the tow weight if I wanted! I am going to upgrade the hitch to a 7500lb version just for the extra capacity. We tow a 13 Explorer now and I may get a 1/2 ton pick up in the future and that will allow me to tow that safely.