You proceed calmly, that's what you do. You notify your tenant (in writing) that the notice to quit stands. You request that if your wife contacts her again re moving out that she (tenant) is to contact you immediately. You need explain no more than that.
You refer to 'my' tenant, so I presume that the cottage is a pre-marital asset in your sole name and under your sole control. However, if it is in joint names or could be considered a marital asset then I'd assume she has just as much right to cancel the notice as you have to issue it.
I suggest you get yourself to a solicitor asap, often these things aren't as clear-cut as they seem to be. You should anyway since you are planning to divorce, but you want to be sure you are in completely legal territory wrt the cottage. If it turns out that it is a joint asset, you may need to start divorce/separation proceedings in order to bar your wife from cancelling your notice.
As far as being 'trapped forever', you are not 'trapped', not unless you want to be. A SAHM with young children, no income, and no support nearby is 'trapped'. You have income and you have a business, so stop panicking! I daresay there are myriad ways to keep out of her way if you really want to. Don't get drawn into the 'drama'.
I'm sorry to be harsh but get your balls out of the kitchen drawer and start acting like an adult instead of a frightened little child. And yes, I'd say the exact same to a woman in your situation. Except I'd be telling her to get her ovaries out of the drawer! And lest you think I'm talking out my arse, I've been where you are (except ex was abusive, not a cheat) and I can tell you that you need to stand tall and be determined.
BTW, do your DC know what's happened?