I am so sorry this has happened to you OP. I'm sending a virtual hug.🥰
I don't know what it is about children and men, but many seem to have a problem when their children come into a relationship and it's not about sex but that's used as an excuse.🤔
Sure things change when children come into the equation. But nit just for dad's. Mums tend to pick up the vast majority of caring responsibilities, so it means we have less time for everything else - cleaning, our partners and ourselves.😬
But into practicalities, call the estate agent. Tell them what's happened. Ask for the property to be marketed for rent - they can discuss with the landlord to arrange this. Once a new tenant is found you can leave - really not sure why you didn't go onto a rolling tenancy tbh versus starting a new 12m one, but that's a mute point.
Sign on at DWP unless your on maternity leave.
See a solicitor and get the finances sorted.
Once you know there's a new tenant found you can pack you and the children up. Go stay with your dad - he has more room. We used to use our conservatory as our lounge. It was fabulous, so you should be able to use it as a bedroom. If it's cold get some window film, attach it to the window and use a hairdryer to create a taught seal. This is like adding an extra layer of glass, so will keep it warmer. Use an electric blanket and infra red heating only when you need to.
Noone is saying any of this will be easy. 17 years of a relationship is a long time to out of the blue walk out, but it's happened 😞
Good luck OP, lean on friends and family, you need them x