As I understand your question, you want to replace your 9200 BTU air conditioner with a 13500 BTU.
If this was all there was to it, I'd say no problem, but I would be doing you a disservice. I work in a camping resort and I encounter troubles with guest's AC all the time. And this may not apply to you ... but here is the problem I see. Many coaches come into our park loaded with equipment from the manufacturer and the owners pile on more. Many are equipped with a 30 amp service. Thirty amps of power is one TV, one Microwave and incidentals - OR - One TV, one A/C and incidentals. I'm my experience, it is pushing the envelope to try to run a TV, AC and Microwave and incidentals, 30 amps will simply not support this load.
If yours is a 50 amp service, you probably will not have this trouble.
If your AC is on a dedicated branch circuit in your coach, it is probably a 15 amp. A 13500 BTU unit should also run on a 15 amp circuit.
When my wife and I encountered the inadequate AC problem you describe, we made the coach "smaller". We closed off the bedroom and bathroom and the AC was able to make us comfortable on those few very hot days.
I appreciate the opportunity to address your concern and I hope my response is helpful for you.