Don’t lie (that is such a bad idea in every aspect of BS application). BS want to know that your parents are supportive of the idea. @buuzn03 gave you great advice and I would follow her suggestions.
Regarding the awkwardness of zoom - stop worrying. Everyone knows zoom is awkward. No one doing the interviewing will care if they ask to speak to your parents and you say “great I will go get them for you” and then you get up and go find your parents. You guys are trying waaaaaay too hard to be polished and perfect. Trust me when I say that is not what AOs are looking for. My son spilled an entire cup of coffee at one school during his interview. Guess what, he still got in. Take a deep breath, they expect you to be human. You don’t need to contort yourselves because of zoom.