Your DH isn't treating DD1 as his own. He is the problem. You are a family. He wants to give DD2 opportunities he's not prepared to finance for DD1. Personally, I wouldn't accept that. He can't make his family treat DD1 the same and as family but he bloody well should.
The inheritance thing I understand. He will leave his money to DD2. You will leave your money to DD1 and DD2. DD1 has her own paternal family she will inherit from.
I dint think it's unreasonable for MIL to want to spend the occasional day will DD2 alone.
The family photo is what it is. I think you need to explain to DD1 that all family's are different. You are a blended family. This is DD2 family because its DD2s dad's family. Her bio family is your family and her dad's family. Sometimes DD2 will get gifts/ trips that she won't get and vice versa.
Make sure your will is water tight so DD1 definitely inherits from you. I have a few friends who got nothing because there parent dies first and the step parent inherited and then left all the money to their bio kids.
In all honestly I don't think I'd continue the relationship with DH. He doesn't seem to accept DD1 as his.
I personally don't want a step anything daughter, son, niece, nephew. I've done it before and got hurt. After 14 years of treating the kids as my family the relationship broke down and I was told the kids aren't anything to do with me. However, I wouldn't be cruel. I think not inviting DD1 to the wedding was cruel.