Wow- being divorced myself, with an ex who is remarried and expecting a new baby and my own husband and my 10 year old son... I know how complicated and emotional these issues can get, even when everyone is TRYING to get along and do right, etc. If one person IS NOT, or is taking advantage, etc. it just makes it harder.
I don't doubt that you've tried to be the bigger person and be a good stepmom. It must be very difficult for you to see your stepdaughter not appreciating her dad or taking advantage of him. You don't say the girl's age, but if she is a teen, you have to remember that lots of girls have these issues with their parents at that age, divorced or not.
If her mom has just had a baby, this girl probably is having a difficult time- again, even in the most perfect circumstances, a new baby can really disrupt a family. I have to say, I applaud your stepdaughter not taking the easy out by coming to live with you and wanting to help her mother out.
I agree that your husband should have talked with you about this first. But- maybe he was afraid you would say no? Or maybe he just assumed you would also say yes? Either way, you should discuss that with him.
But before you do, search your heart. Yes, it sounds like his ex is pretty irresponsible and has made some poor judgments and continues to make them. But - that will NEVER change the fact that she shares a child with your husband. IMO, he was doing the right thing- both morally, and as a parent, by allowing them to move into your rental.
You don't say what your financial situation is. If you really need rental income from that house, I can see where this would make you nervous from a practical standpoint. but again... would you really want this woman and her baby and your stepdaughter in a shelter when you can do something about it? I know you want to protect your husband, but it sounds like he was motivated to help them for the right reasons.
Look in your heart- put yourself in the other person's shoes. YOU have won- you have a good marriage to a good and generous man. What does this other woman have, besides a new baby to care for and no where else to go? If you are religious, talk with your pastor about it. We always have so many 'worldly' worries- paying the bills, going to work, etc. that sometimes it is easy to let them overwhelm our moral generousity.
I am not saying let her freeload forever. But talk with your husband and set some goals for your stepdaughter's mother to meet as far as payment, getting back to work, looking for a place, etc. Remember that she will ALWAYS be your stepdaughter's mom and this girl is looking to you and her father for help and will take her cues from you on how to treat people when she is an adult.
Set the kindest, most helpful example you can. I KNOW it can be frustrating- but you just need to dig a little deeper for that 'bigger person' inside you- I know you have it in you!! Good luck!