Hi, this sounds very similar to my situation! I was with my now ex for 15 years, we have a 6 year old together. Our relationship deteriorated over many years until I finally ended it. It’s the hardest thing I’ve ever done. He decided he wanted to remain in the home that we both owned, so he has paid me my share of the house, which I have put down as a deposit on a new home for myself and my daughter. Speak to your mortgage lender.
We waited a few months before telling our daughter, until we’d made a plan and got our heads round it a bit.
The main thing for us is that we agreed from day one that, no matter what, our daughter comes first. We have managed to maintain a pretty amicable relationship for her sake.
Be kind to yourself and take it one step at a time.