Force sale of house????

Hi there, I''m new to this site and not sure if I''m posting this in correct forum……I''ll let you know what my situation is regardless and hope to hear from anyone who can help.
I split with my girlfriend of 14 years a year ago on August 1st 2011.
We have 2 children 13 and 8 and she lives in the home. I left the home after she said i could live in a flat she owns (bought while we were together but in her name only) The idea was she would sign it over to me in April 2012.
I moved in and with the intention of owning it I spent about £3500 doing up the flat……I have now today been given 2 months notice to leave the flat.
The family house is owned by both of us, I am paying the mortgage and on title deeds. My question is….can I force her to sell the house? As I will now be homeless?
The house has around £240,000 equity and I wonder if the share would be more favoured to her.i.e 70%- 30% or something similar because she has the children live with her.
She has told me I can take her to court and battle it out for years and it will cost me a fortune.
You''re probably thinking she''s upset I left….It was her choice, she was having an affair!!
Any advice would be much appreciated….

Unfortunately I am in North Carolina at the moment nursing my sick wife.
If you are unmarried, the probability is that you could force a sale but it is likely that the sale would be deferred until your youngest was 18.
To determine your share on eventual sale, you would need professional advice. Really, this is an issue that should have been addressed when you bought the property. The title deeds should spell out what your interest in the property should be.
LMM