To change his Tstat to a digital may require a new upper board. RVP and Dometic tstats rarely fail by NOT cutting off as in his first post and he has already replaced it is a VERY rare problem. His system does have a 2 to 3 minute delay to keep from short cycling the compressor and causing breaker trip. He needs to post
1. year of RV
2. Model of AC
3. P/N of his tstat
Odds are his wall tstat is NOT sensing the inside temp because there is some heat source transmitting excess heat to the back of where the tstat is located. This can happen when they mount the tstat on a sidewall cabinet of a refer of on the inside sidewall of the RV. Doug