As many rig riders will tell you a sidecar is a very different beast . The closest thing it could be related to is a snowmobile. Yet that still isn't a very good analogue.
Sidecars don't counter steer when all 3 wheels are down. But they immediately revert to countersteering once the wheel is "flying " or up off the ground. That's where novices get into trouble.You're pushing right to turn right and if its too severe and the wheel comes up then the bike is leaned over onto the side of the tire just as it is in a left hand turn and suddenly you're going across the road. And experienced rider can feel the tipping point and control it through the throttle, shifting weight to the sidecar frame or both. Most rig riders keep ballast (about 50lbs) or so in an empty chair.
Don't get me wrong, i had a chair for 15 years and loved it. I rode is solo plenty of times but its something you need to learn about before getting involved with it. Especially if you're going to be carrying a loved one in there. But there are plenty here that will answer any questions you might have. just ask.