You are getting some very good advice here already so I won't repeat all the same things, but I agree 100% with AS. At one point my EW proposed an 8 week separation, but it was BS that the MC had suggested, and she had no intention of staying in the MR. I think it can also be seen as a way of letting you down gently rather than all at once.
I was very lucky in that I moved out of the house right after BD, but was able to get back into the house 4 months later. My EW, for all of her defects, was a woman of her word, plus she felt/feels extremely guilty about destroying the MR. However, that is a rare case, and I think it would be even more unlikely to happen with children involved. No matter what, you should stay put - not because it will or won't help you salvage the MR, but because it is the best thing for you and the children. She might file right away, she might linger in the house for a long time in IHS, or she might move out. But that's all on her, not you.
W 34 Me 42 Married 7 years together 8 0 kids 1 beloved dog BD 4/6/2018 I moved out 4/7/2018 I moved back in alone 8/05/2018 I file 3/06/2019 D official 5/7/2019