Yes, this is exactly what the Wyze Cam was designed for, monitoring an indoor space. If you’re planning to use it for interaction you might consider the Cam Pan so you can always get the best view of what’s going on, especially kids that tend to be all over the place :).
The app has a Live View mode that shows a live stream with audio and the ability to speak through the camera (with a short delay). In my experience the audio is a bit muffled but if someone talks clearly within 10 feet of the camera you can usually hear them.
The camera connects to your home WiFi (on the 2.4GHz band specifically).
I assume you have already but if not you’ll want to clear the 24/7 surveillance with your wife :). My cameras are only allowed to point outdoors