Piper,
If the two headsets aren't compatible then you'll have a problem setting the voice-activated squelch on the intercom, in many cases.
A sock around the microphone helps with airflow over the mic in some cases, but not all. Impedence matched communications systems, using the same type of headset (and especially same type of microphone) help. Some headsets will even break squelch when sunlight strikes the microphone.
For now, all you can do is turn down the squelch, or VOX sensitivity on your intercom system. You'll find that better intercom systems will give better performance, too.