Ah ha ... Right your job is to show her then excatly what separation means !!!!!!!!!!

No coming over to the house when she wants. Set rules
Not included in day to day activities of kids.
No help financially
No family fun

This may seem harsh on your kids but it is a situation not of your making but one which you must create stability.

Physically there might not be to much change for wife and kids BUT emotionally and mentally it could be huge for HER. Not your kids because they have you.

If she leaves you have to show her how much she is missing. The consequenses of her actions and no doubt Affair.