This situation is part of coping with blended families. I have seen a dramatic increase in the last several years with exactly this issue. I am glad you asked about this emerging problem.
Your husband is enabling his daughter’s behavior by excusing the inexcusable to assuage his own guilt. This makes the situation worse, not better.
His daughter has everyone and everything in orbit around her. This is not good for you or your husband, and it sets up a very dangerous precedent. Her inability to appreciate the needs of others is deficient. It is easy to predict what will happen. She will systematically be dissatisfied and use anger and intimidation to try to force people into doing what she wants. The impact of this is to eventually alienate herself from others. Some of this has already happened. You leaving meets her needs, but destroys the relationship between you and her father. In the long run your husband is likely to end up with a poor relationship with his daughter, and none with you.
There is nothing you can do but exactly what you have done. This isn’t your issue to fix, and by setting a boundary for your husband’s lack of responsibility in this matter you have left the issue where it belongs: with him.
If it were possible to get in to see a good family therapist I would make an appointment as soon as possible. If not, couples therapy would be a good idea. The find help tab above will help you locate one in your area. But the child psychologist was exactly right. If your husband doesn’t change his behavior with his daughter, there is little to go back to.
Wishing you patience and peace,