Yes she is WW she just admitted it to you. I also agree with her as I also got the feeling the selling the house was a ploy on your part to get her back. IMO after everything she just told you , you need to go in the opposite direction. Accept that tour marriage is over for now and build an awesome life for you and your kids. If you pursue in anyway this will make you look weak and pathetic.
This isn’t over you are still early in the process. No more talks and definitely no pursuit.
This $hit ain’t easy but you will survive and thrive if you choose to.