I'm just going to give my opinion and others can correct me if I'm incorrect.
Most mobile RV techs are able to work on your "house" or coach a/c --typically located on the roof. However, you are describing automotive a/c and I believe (again, not completely certain) that special certification is needed to "officially" service automotive air conditioning.
See this link:
EPA Regulatory Requirements for MVAC System Servicing
It seems to say that service people working on motor vehicle air conditioning must be certified to handle refrigerant for automotive application when doing it for money.
Now this is not to say that a mobile RV tech won't have that certification but many that I've come in contact with are NOT certified to service automotive a/c.
Therefore, I think your best bet would be to find a general auto mobile mechanic that is certified to commercially repair and recharge auto a/c systems and then contact each to see if they're okay with working on a motorhome.
Here's a few suggestions from doing a quick online search that you can contact and inquire just in case nobody chimes in on this thread to specifically recommend somebody:
Mobile Mechanic of Houston - A/C Repair & Recharge
Mobile Auto Repair Pros -- Heating and AC cooling services
Ace Mobile Mechanic -- AC Failing in this Texas Heat?
Houston's Best Mobile Mechanic -- A/C Certified
From "Your Mechanic" (who knows of the reviews are legit or not ...?):
Ben -- see reviews from Berry on October 19, Virginia on July 25, Steve on Aug 01
John -- see reviews from Alan on October 19, Brian on May 30
Breck -- see reviews from Laura on April 14, Charles on July 31
Anther alternative would be to use a mobile semi truck repair service but I'd have to believe that it would be much more expensive. For example, these guys work on RVs too but do have a mobile service ...usually, though, a semi truck mobile service is much more expensive as they consider it "emergency" mobile:
Southern Truck Repair & Service - Complete A/C repair and recharge services
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