Can I run 15,000 BTU air cond with RV plugged into my house?

The only way to do it is to do it right. Have an electrician run a dedicated 50 amp service from your box, to an outside outdoor rated box. That way you'll be able to run everything and not worry about tripping breakers. Now your running off 20 amps, and if you turn on anything else thats on the same circuit it will trip the breaker. That plus the length of your cord, on 20 amp service will give you nothing but problems.
50 amp service with a 50' cord should be no problem at all.
Grumpy