This isn't about your SD at all, it's about your DH. BM didn't teach her this, HE did. He has played Disney Dad and parented out of guilt, and SD is the person that type of parenting and dynamic created. Don't be mad at her, be mad at him. His actions have developed and encouraged her behavior, and shaped the relationship dynamic they share. It also pits you squarely in the corner of "outsider", so DH never has to take responsibility for any of her unhappiness, he has you as the perfect scapegoat!

Honestly, you are placing blame on the wrong party. That's like the spouse who got cheated on blaming their partners infidelity on the "other woman".

"How do I to talk to him without us getting onto a fight?"

I don't think you can, unfortunately. You said you've talked to him before, it does no good and he just gets upset. The thing is, you can't control anyone else's actions or reactions - not your SD, not your DH. The ONLY person you can control is yourself. So what do YOU need to do? Tell DH not to tell you what he bought her. Don't be around when she's visiting, go find something else to do with friends. You can't make her stop taking Daddy's money, and you can't force him to stop giving it to her. All you can do is stop how it's affecting you. (If it's affecting you financially, then keep a separate bank account, one he can't take money out of for her.) Sorry, but I really think that's all you can do unless you want to fight with him - and as you've discovered, fighting with him about it doesn't actually change anything anyway.

I have the same problem with my eldest SD..now in her 40's...The problem is, when the bio parents overcompensate out of guilt and teach their children that love is defined by how much materialism they give their child.. (they both got caught up in competing for her loyalty by buying her things and trying to outdo each other)...
Unfortunately.the child grows up thinking...if you love me then you will give me something...My SD cannot invest any time into our relationship without expecting to be given something in return...She seems like she is dissatisfied with just being able to spend time together...she acts as though we have to prove our love by giving her things...The other part of the problem is, when a parent goes 150% of the way in the relationship for whatever reason...all the time..it sends a message that the parent is always the one doing the pursuing...The parent owns the entire relationship...rather than have a relationship between two people based on what they each contribute to the relationship...so the culture is one that creates a one sided relationship...If your DH wants to groom his daughter to be sold to the highest bidder...then tell him he is doing a great job...because when she pick out a spouse..the same unrealistic, unsustainable, expectation will be put upon him to fulfill a never ending appetite that is never satisfied...because self is never satisfied...and is doomed for failure...I have watched my SD go through 3 marriages now and it is so sad to see her teach her children the same belief system...

If your DH really loves his daughter...he better get some counseling on this before it is too late...He has taught her the wrong definition of what real love looks like...He has also taught her to have unrealistic expectations of what a healthy relationship looks like...If he doesn't change...She will pay the price and end up one unhappy miserable human being for it...

I think a lot of times divorced parents are so busy trying to win the short battles against each other...that neither of them step back, look at what is best for the long term for their children...they don't relate to delayed gratification...they are too busy trying to win the right now....in the long run it costs them their children, and they don't see it until it is too late....