As waltermitty said, a Cessna 150 that is IFR equipped is going to be your best affordable option for what you describe. You would have to have more guts that I do to fly a 2-stroke powered plane at night or IFR. These engines were designed for ultralights and other very light planes. They do not have the reliability or the electrical systems needed for night or IFR flight, and I dare say you will have a hard time finding a 2-stroke powered plane that is IFR legal.

Similarly, auto-engine conversions do not enjoy as good a safety record as certificated engines. That is just a fact. I personally know of five inflight engine failures of auto engine airplanes. These have their place but it is not at night or in IMC.

$15K is a pretty tight budget for what you are trying to accomplish, but don't get sucked into something that isn't safe just to save a little money.