Make your offer on the second house contingent on the sale of your existing house. This happens all the time. Most people are not in a position to be able to do it any other way.
I don't feel you are in a position to be able to keep your existing house. And the rental business is a crap shoot. I have owned as many as 5 houses at the same time (including the one I live in), but only rented one out. Learned my lesson on that one. No offense intended to anyone, but renters generally have a strange, selfish attitude, and treat your property like crap and they dont give a rip about it.