Towing with a class c?

It is legal if the combination does not exceed the size limits for the place it is being driven. One piece is a truck, another is a trailer. There are well known size limits for trunk highways, varying state by state. There are lesser limits for specific streets and roads, in states where localities have authority to set limits.

For road legality, doesn't matter whether or not you can live in the vehicles.

Whether or not you need a CDL depends on what you are doing with the vehicles, not what kind of vehicles they are or how you combine them. RVs are presumed in most states to be private, non-commercial vehicles. Some states require you to get a different class of non-commercial license for assorted weight and length combinations. In most states, this is much larger than a typical class C, or the TT a class C would be rated to tow.

I just towed my 28 ft travel trailer with my Class C. It's not something I do on a normal basis. Luckily the TT weighs 4400 lbs. class C max tow weight is 5000 lbs.
Texas Law
Vehicle Combinations
Texas Transportation Code 621.205.

A combination of not more than three vehicles, may be coupled together if the combination of vehicles, other than a truck-tractor combination, is not longer than 65 feet.
A passenger car or another motor vehicle that has an unloaded weight of less than 2,500 pounds may not be coupled with more than one other vehicle or towing device at one time.
A house trailer or towable recreational vehicle and motor vehicle combination may not be longer than 65 feet.

In Calif you can have a total length of 65ft with a regular drivers license.

In most states, this combnation should not be a problem. Only thing that may effect legality would be the overall length.