If I don't move out, she says she will take the kids and move out. Should I be ok with this?
I totally agree with RegretfulLA. You might want to read Dobson's Love Must Be Tough, it dovetails with DB in that he says if the spouse threatens to leave then you support them. Validate their emotions- say that you understand why they feel that way and you support their decision to leave. Often the WAS feels trapped and caged, and when the cage door is thrown open they're suddenly not to sure they want to walk out.
As RegretfulLA said, do not leave yourself. Your W needs to make the tough decisions and she needs to live with the inconvenience and ramifications of those decisions.
You should negotiate visitation with the kids, it's not fair of her to threaten to just take them away without working it out with you. Things have to be negotiated in a separation and it should be done as amicably as possible.
Separation is not the end of the M. It may be a needed step towards reconciliation.