I don't see a romantic relationship here. I see two resentful adults saying "it's for the best" as they avoid conflict resolution in the name of children, who are old enough to sense this bitterness, and will have it effect their whole lives.

You want counselling? Book an appointment when your wife is free and take her. No mentioning how stressful, etc. Recognize opening the can of worms is always harder than leaving it closed.

It is really sad to see you describe this whole thing. Like you are trapped and angry and exausted when you two have lifetimes left to live.

Show your children that there are efforts and steps to take to solve conflict and be a loving partner. Take your wife on a date. Take your kids somewhere fun, or ask what theyd like more of.

When did you stop feeling like a person and only like a parent? :( How can you repair things when it sounds like you are at odds with your wife...?

This is a firm tone but I think you can fix things if you are ready for work and being humble. You cant say you are fine with your wife leaving one moment, then say you are willing to try if she does. Prove it! Show her! Show YOURSELF.