What rights do I have regarding shared custody with my common law partner?

I found out she was cheating on me for eights months while we were living together. And to top it off she was having a fling on facebook during the same time with someone else. She was bringing our child, 15 months at the time over to his place and he was coming over to my house at night while I worked. We still live together and I've been the primary care giver for over a year. Now I'm worried she will leave the province with her after we sell the house in July. What do I do? I plan on getting a lawyer soon, but need an idea what I can do. Thanks..