How to Get What You Want in Life/Love or loss
I want to marry my child's mother we have been "dating" for 9 years and my son is 3. We broke up 5 months ago and she has had sexual contact with another man. She is still living in the house with me. She often tells me that we can never be back together, yet she has not left the house. What is it that I need to do to show her how important it is that we rebuild our relationship?
You have not given a lot of information about your relationship, however I can evaluate as an outsider and give you some points to consider.
You accept the relationship has broken down and she appears to be moving on. The question is what went wrong and is it repairable? The only way to see if you and her can get together is to open communications between yourselves. If she is not willing to talk, whether with a third party involved or not, such as a marriage counsellor, then it will be very difficult for any changes to be made.
If she agrees to talk then you need to find what the issues are. Try to avoid arguing and focus on behaviours rather than attacking the person verbally (e.g. I don't like it when you ... rather than you are a ...). Although you are the one who wants to mend the relationship make sure you look for compromises for both of you. If she is willing to talk but still wants to end your relationship then for the sake of your son try to approach the situation maturely so that you can work out solutions that will work in the long term.
The fact she has not left the house may be down to a variety of reasons. Moving is stressful, difficult and requires work. Perhaps she likes the house, has no financial means to move or believes she has a right to stay in the place for your son's sake.
Whatever the issues I hope things work out for you.