That definitely sounds like an EMC (Electromagnetic Compatibility) problem. There are probably at least as many causes and cures as there are airplanes flying, but as has been suggested checking your antenna and feed line is probably a good starting point. Not just the grounding of the feed line (co-ax) at both ends, but the resonance and impedance of the antenna as well. (Find a local Ham Radio Operator and borrow a VHF SWR meter.) It would be good to monitor the 12 Volt system as well, because it is possible that when you key the radio it is causing a voltage drop to the instruments and AP. Check all of the grounds of the affected instruments. Do they, by chance, ground at a common point? It is also possible, though not likely, that an RF filter might be needed for each of the instruments. Just keep checking until you find the cause. The fix is usually easy once the cause is uncovered. I make my living preventing and curing problems like this, and believe me there is no magic fix. It is an iterative process unless you get very lucky!