I can sort of understand how your MIL might feel. If your dh is not fully in the dad role (which you did not mention this) and DD2 spends a fair amount of time with the real daddy, then she probably feels more like a step-grandparent than like a real grandparent.
Here are a couple scenarios, not sure which your situation fits in. My brother insisted we pretend his stepchildren were the same as if they were his own children. But it went one way. The stepchildren were not expected to act as if they were our nieces and nephews or cousins of our children or such. In fact, when one of them got married, we were not even invited to the wedding. That was the oldest and she got married maybe 2 or 3 years after my brother and his wife got married. The stepchildren had a dad and they had grandparents from their dad and they most certainly did not need a 4th set of relatives. They made this very clear to us. The youngest of the 4 kids is much more polite than the rest. But she is so stressed over this that I recently found out that the reason she lives with her boyfriend with no plans to marry is that she does not want to deal with the drama of who the real dad is. She was actually only a grade schooler, early grade school in fact I think, when my brother and his wife married. Fact is, while she was the child of the last marriage prior to my brother's marriage to her mother, the others had lost a relationship with an entire side of their family when their mother left her first husband and then the 2nd husband, and I think there was someone else in between, but am unsure.
But, a grandparent should be allowed to fuss over her grandchild and love on her, without being obligated to do 100% equal for a child who thinks of the older person as their stepdad's mother rather than as their equal grandparent. If the child gone every other Christmas, every other Thanksgiving, with her "real grandparents?" If so, then it is completely understandable and acceptable how your MIL handled this. (assuming there was not outward rude remarks or such toward the stepchildren)
The other type of situation, though, is where, for example, my cousin married someone who had a little boy. The boy's father was out of his life pretty much. The boy visits the grandparents as much as the biological/adopted grandchildren. The boy thinks of the grandparents and cousins and such, as as his real cousins, because they really are. Technically, he is a stepchild, as in, my cousin never adopted him. But the relationship is the same as if the child were not a stepchild. My children call him their cousin. I would consider him to be as much a relative as any one born or adopted in to the family.
See the difference?
I hope I have explained myself well. Since I am not sure which the situation is, it is hard to make a call on things. If your dh can adopt your child, then you will show that your child from before the marriage is just as much your dh's child as your child from this marriage. It will also solidify any relationship so that your MIL does not have to feel if you two divorce, she will never see that child again.
I am curious though, you said your 2nd child lives with you and that is the one you are upset about. Where is the 1st child?
Good luck with the situation!