Deal or No Deal

4 years ago my partner left me and took the kids leaving me with the mortgage, bills and debts. We managed to stay friends and have since become best friends again even though she is in another relationship and is expecting a child in April. I have been on debt management since then but things are starting to get a bit tight again financially. Neither of us want to sell the house as we both agree that it would be beneficial for our children in the future. However, as I am finding it difficult to keep up with the cost of keeping the house, and she is in need of a bigger house, SHE has come up with a "solution" which sounds like it could be beneficial for both of us. At first I agreed it was a good idea but am now having doubts. She has suggested that if I were to move into cheaper accommodation (which basically involves lodging at a friends house) then her and her new partner would take on the house and pay me "rent" equivalent to the mortgage as the mortgage is about the same as her current rent. They would pay the bills on the house leaving me with the ability to free myself from debt a lot quicker. Woo-hoo! My concern is that if I move out and allow her in would it then be possible for her to claim ownership of the house as my children will be living there? I am happy for her and the children to live there as it would benefit both her and the children being closer to school, town etc. and the thought of being debt free after all this time is also very appealing. I could afford to take the kids on proper holidays, buy a car that doesn't need repairing once a month etc. BUT I am not comfortable with the idea that she may just be trying to steal my house from me. I am stuck between a rock and a hard place and need help on this urgently as she is pressuring to get it done ASAP. Is there a way? Can I let them live in my house without risk of losing it? I just want to do what is best for my kids but fear I could actually be losing more than I already have.