Good noise suppression is based on the device getting input from microphones near your mouth and elsewhere, so it can figure out which sounds it needs to keep and which are noise. The farther it is from your mouth, the less capable the voice suppression is going to be. Two people sitting next to each other is a fairly difficult situation for any noise suppression system. Some standalone mics are better than others, but none of them will do as good a job as a headset with a boom that puts the microphone near your mouth.

If you refuse to wear a headset, the Logitech Blue Yeti is probably your best option in that price range, although you'll have to find it on sale,

Headsets have a well-deserved reputation for being uncomfortable, but there are plenty of exceptions. Normally I would recommend one of the lightweight office-style headsets for maximum comfort, but you will hear everything your wife says with one of those, even if your mike doesn't pick it up. What you probably need is a good over-the-ear headphone with a good multi-pickup boom mic.

Most of the headsets that meet your needs are designed for gaming. Many will have features you don't need, but "business" headphones tend to be even more expensive. Unfortunately, I don't know of any that I would recommend in your price range. You would probably need to double or triple it to get something that really does what you need.

I hope you're able to find something that works for you.