OP your DH's BM is in her late sixties now. She is of the generations in Ireland who felt terrible shame for having a child out of wedlock.
I also watched Philomena recently, Philomena took 50 years to confess, if confess is the right word, that she had a child out of wedlock in 1950's Ireland.
My auntie had a child out of wedlock in the 50s also. My GM locked my aunt up in Magdalene Asylum and threw away the key. It was only my mother who saved her, she forged my GM's signature, got my aunt out of asylum onto Dublin and put her on boat for Liverpool. My aunt's baby, my cousin was adopted to people in the US we think.
My aunt went on to get married and have a further 7 children.
My mother told us 10 years after my aunts death what had happened.
Get this:
To this day my mother WILL NOT let me or my siblings tell our 7 cousins what happened to their mother and that they have an older brother who could still be living.
I have asked her time and again, that they have a right to know, that they would be grateful to my mother for saving their mother, all to no avail. 
She is adamant, she does not want them told. The SHAME is just too great in my mothers mind. Such was the hold of those evil people in Ireland.
OP I know your DH must be upset, really upset but please just let this rest. Forcing the issue would be a mistake I think. Maybe with time his mother will come round to the idea, but dont get his hopes up too much. Maybe just send her cards, photos etc to leave the door open.
As for whether you symphatise or not with her, I'd leave that be too. You really dont know what she went through.