to clarify-- I do not think you should nest either (or at least, if it was me, I would not nest). When I said you can't control her, I meant you can't force her to do anything-- stay, go, be a happy wife, etc. Just like she can't force YOU to go or to nest.
If I were you, I'd spend some time really, really thinking about what YOU want.
Do you want to stay married/stand for your marriage under the current circumstances? No one here will judge you if you decide you can't. But this is critical information for you to know yourself and for folks here to give you advice based on your goals.
She can't force you to nest if you don't want to. If she wants to leave, she can leave. If she doesn't want to go permanently and you decide it is too painful/hard to live under the same roof as her when you are separated (remembering that you can't control her behavior), then you can choose to move out yourself or to nest. It is up to you. Your primary responsibility is to be the best dad you can be for your kids. If you think that nesting is the best way to do that, then by all means, but I would read the experiences of others really carefully. Be very very sure you're only doing it for your children and not out of a secret hope that it will result in an R. Like Sage says, it can be really difficult for the children-- and for me, I really felt like if we split, I was going to need to really focus on my own mental health and healing in order to be the best mom I could be. Nesting (or really any contact besides the bare minimum) wasn't going to help me heal and move on.
If you decide you don't want to nest and you don't want to move out yourself, then you just tell her-- hey, I've thought about this some more, and I'm not interested in nesting. I don't want to divorce or separate. I understand this is what you want, but I don't think nesting will be good for me or our kids.
Me (46) H (42) M:14 T:18, D9 & D11 4/19 - 12/19: series of escalating BDs 9/20 - present: R and piecing