How do you leave a 10yr commonlaw relationship with 2 kids and a boyfriend who just change his ways in order to make it work because he knows am seeing someone else.

If you aren't going to be faithful to him and work it out with him then you do need to break up.
You need to decide if you really want to keep cheating on him or work it out and then write a pro and con list on what you need to do.

Like him move or you move
What makes you think it will work with the other guy
What you can do to work on your current relationship and why you think it won't work
How the kids are going to deal with it
How are you going to make it possible
etc...

It's not a question of law.

If the feelings are no longer there, then you're just prolonging the inevitable.

It all depends on WHAT you WANT and HOW you FEEL?