The two primary parts of this situation, if I understand it correctly, are:
1) Your wife does not want you to be with Kim the way you want to be with Kim - period.
2) You have feelings for Kim that are pretty urgent. So urgent, that not "going there" feels like a pressure cooker to you.
These two parts are pulling at each other and causing stress within you and between you and your wife. It's time for you to reevaluate your life, and decide what is important to you. Keep in mind, healthy change is a step by step process. Your urgent feelings want you to fast forward that step by step process. Just because your feelings are urgent, does not mean acting on them as fast as "they" want you to will improve your life.
You have an urgent want, and your wife is saying no. This may be showing you that you and your wife may no longer be compatible. There are times when one person's interest in poly is the catalyst for the relationship to end.
The best thing you can do is acknowledge your urgent feelings, but don't let them make your decisions for you. Reacting to urgent feelings rarely improves a person's life. Take the time to look at which one of the options, that are realistically available to you, you want.