Eli,

You are seeing someone who lies to his wife and others, someone who has cheated on his wife before, someone who does not seem to care about his children/family.

Check you own personal values and see if you wish to continue in that relationship for you are complicit in helping to create that.

It is easier to decide on expediency rather than morals and values.  It will be good to get clear on what are yours so you can better informed decisions on your life in general.

Mark