I'm still kinda new here. How does one say no exactly? I don't really see how I can expect any cooperation here? Shall I move out and give up the house? Shall I ask her to move out and buy her out? Isn't this what's best for the kids? The thought of uprooting them so fast seems so harsh.
Constanza, as Steve says, becoming assertive (controlling you, not controlling her) is simple. You don't move out. You don't date other people. If and only if she asks--"No, I'm not moving out." "No, I don't want to date other people." No big talks. No big arguments. The kids continue to have their home. The kids continue to see you everday. You don't want her to, but she's free to move out, or date other people, or eventually file for divorce and a proposal to split the family home on her timeline. These are her problems to solve on her own as she likes and on her own timeline as she wants to end the marriage and you don't. Your focus on being the best constanza you can be. That's your Hail Mary.