Recommendations

Before you but anything else I'd look into thresholds of when your mic actually records. You might be able to just change a setting so the lower volume of your wife farther away just isn't picked up.

Most videoconferencing software these days has dynamic gain to try to accommodate people using non-ideal microphone placement. See if you can turn that off. Audio pressure decreases pretty drastically with distance. Using 10 cm as your microphone to mouth distance, 2.5 m as the distance from your wife's mouth to your microphone, and 60 dB speaking volume, your voice is 30 dB louder than your wife's. That should be enough to make it nearly inaudible / certainly not distracting.

If you're looking to mic shop, get a directional mic. Your current microphone is omnidirectional. A directional microphone will provide even more acoustical attenuation over your wife's voice. A coworker uses one of these for his WFH setup. Look for terms like Cardioid, Supercardioid, and/or Hpercardioid. These are the same microphones used by vocalists on stage.

First off, do not buy a blue yeti, ever. They are microphones specifically marketed towards streamers with disposable income and are, all told, Not Great.

Unfortunately, the fact you don't want a microphone right in front of your mouth, your budget, and your needs are at odds, so you'll have to compromise on one element. You're already compromising on the needs, so that's out, and you have 2 options:

• a condenser microphone is the search term you're looking for, but they require being quite close to your mouth if you want to avoid ambient noise. They generally require an external amplificator to connect to a PC, and that's costly, but I think you could fit both in $100. A condenser mic that claims to not need an external amp is probably not really a condenser mic (though they exist, they're expensive)

• the alternative is a shotgun mic. These don't need to be right in front of your mouth due to wave dynamics engineered to only capture sound in front of them. They're frequently used on cameras, to capture the sound in front of it but not behind. They're also really expensive and will definitely need external amplification.

Unfortunately for you, this exact problem is of particular interest to pretty much only people who have "a Sony a7 is an amateur camera" money, so all solutions are quite expensive.