I would tread lightly with this new lady. She is living with someone, they may not be married but does a piece of paper really matter when emotions are involved? Be careful I don't want to see either one of you get hurt. I see it as a very touchy situation and her moving from one relationship right into another may not bode well. JMHO and I my just be acting like a over protective parent.
Any time with your D must be just pure heaven. I loved when my kids were 2 to 4 years old. Everything is new and you see the world through their eyes. Its a wonderful experience.
Have a great weekend and take the suckers at your Texas-Holdem game for all their money.