I think his families assessment of a pathological liar is correct, and after six years with him I'm sure you can confirm that also. I seriously doubt this other woman doesn't mean anything to him. Why would he keep in contact with her if she doesn't mean anything to him? He's a liar, and a very immature one too. I have doubts that will change.
You seem to be a sensible, caring person. You've given your partner more than his fair share of chances to get his act together, and you're getting lies and cheating in return. You deserve more than you're receiving in this relationship....and so do the children.
You have two choices #1 Continue in the relationship, which has no
chance of ever becoming a happy positive environment for you or your children. #2 Terminate the relationship, and sever all ties with him, only
allowing contact for child support and visitation.
Your only 36 years old ( just a baby yet! kidding) there is plenty of time to find Mr. Right and get treated with the love, happiness and respect you deserve. You will be an even more loving, affection Mother
when your treated that way, and your children deserve that, do it for them to.