Stay - she should go.
Since it is she that wants to be free, then maybe she will agree to let you keep the kids? Is sounds like she wants to have a different social life, going out, meeting new people and maybe it would be best for the kids to be with you?
Have you asked?
It would make it easier on you, and maybe for her.
The kids may spend lots of time with her, maybe after school, holidays and some weekends, and you will end up with somewhat equal time to love them?
As for you- you sound like a very nice guy. I am sorry to opine that she is not pulling any punches: she clearly told you she is not in love with you. And she hurt you beyond that by attacking you personally. Not a very nice thing to do.
Whether because she is insecure or insensitive and self centered – the remarks stand there as monuments to her views about you.
You know how you feel about her? That is what YOU deserve. Why on earth would you choose to live out your life not being loved and appreciated? Most marriages with love included still have a very hard journey. It is hard to imagine traveling through life with a partner that is embarrassed of you, and does not want to include you in their social life. It just boggles the mind.
Just tell her that you agree to a separation if you can have physical custody of the children and shared custodial rights with generous visitation. One thing both of you should try to do is to remain friends so that the kids see their parents treating each other with kindness and respect though it may be quite difficult quite often. However it is what would be best for the children, so being on friendly terms is best. I hesitate to use this example, but for lack of common acquaintances - think Demi Moore and Bruce Willis?
They’ve managed to remain a family though no longer married. Whether you like each other or not you will remain family; you’re bonded by the kids - but like brothers and sisters and moms and children that sometimes are happier when no longer living in the same house, so parents may also be happier when not sharing the same day to day life and space. One thing you should not do is jump into other relationships immediately as the divorce road is not easy on the kids and is also very confusing.
You can hire a nanny / housekeeper to watch out for the kids until you get home, and to help you all around the house. With a good match, after a while, they become part of your family.
My thoughts only. Good luck. And all the best wishes.
MadArt (ist)
PS: We had a saying in my family: "Better alone than in bad company"
Your life's partner should strive to lift you up, not bring you down - it does not sound like she's very uplifting.