Well I think your MIL sees your daughter, your 1 biological daughter you had with her son, as being HER "only" grandchild.
So she is 'favoring' that one grand-daughter.
I don't know that you can change her construct of that.
She does not feel/see, that your other 2 daughters or the Foster children, as "her" grandchildren.
They were from another man/Husband... and foster kids are not 'hers.'
That is her mentality.... albeit not nice.
Does she favor this 1 grand-daughter in other ways?
With birthdays, Christmas etc., and exclude the other 2 girls as well?
If so, then she is blatantly 'favoring'.
Of course it is not fair.... nor nice.
And she actually does NOT want to do any training, for foster care, either. She is not feeling connected with that emotion nor responsibility nor empathy for it. She does not want to.
You cannot 'make' her feel connected to your other 2 daughters nor to the foster kids.... as you & your Husband do.
So yes, although your expectations are normal human wishes... your MIL cannot feel those emotions. Nor wants to. Nor is able to.
So yes, you cannot "expect" her to be on the same page about it... as you and your Husband are.
I would not... allow only your 1 biological child with your Husband... to be put into this ordeal. I am sure the other ousted kids... feel negativity from it all. Not good. Nor fair to them either. They are not "loved" the same way, by your MIL.
It will create problems for all your children... too. And impact them. Sadly.
But it is also a great deal of expectation... to expect MIL/grandma... to have ALL 5 kids over at her house. That is too much to manage for most adults... let alone an elderly. ONE elderly woman.
And yes, your friend being a "trained" babysitter for you/Hubby, is great. That is a great deed, she is doing for you and your Husband. And to be compensated for it and the training she had to go through... it is only fair that she is paid that.
Also, sure, LOTS of Grandparents do what you described... but it is not their choice sometimes. If you talk to the Grandparents themselves (which I do), they OFTEN will vent about how they "have to" do these things... because the parents of their Grandchildren, don't give them s choice nor even consider their own lives or health problems or mobility problems or endurance or gas money and driving. So, even though they may do these things... it is not 'always' because they LOVE doing it... and they often feel burdened or too fatigued... but they do it anyway.. because for them, otherwise they may not get to see their grandkids... and they are just a babysitter. Or, the parents are just too busy... to do it themselves and the Grandparents don't want to see their Grandkids to not be able to do these things.
all the best,
Susan