When the DOT require a CDL has to do with weights, and."for Hire."
When the state requires a commercial license class is up to the state, despite Federal efforts to harmonize. Some states, it is as simple as the aswer to "am I being paid to make this trip?" There are states where vehicles must be registered commercial if used for business, and an employee driving needs a commercial license.
When I worked in Michigan, I needed a commercial license to deliver cars between our repair shop and dealers' lots, but not to drive a service truck for a vending macine company. That distinction, I thought was subtle, but it had to do with being paid to drive vs driving incidental to my job. Michigan laws may have since changed, but you would be wise to chevk them, as Michigan may still be one of the stricter states on this.
On a one time basis, you might be OK doing the job as a favor.
PS: if resident of Indiana, there may be laxity of licensing to tow RVs, as a concession to the industry. I know they've made concessions in other areas, like requiring dealers to collect sales tax.