Our challenge is that not allowing herself to be held by my MIL didn't start at some "developmentally typical" stage -- it began when she was a newborn, just a week or two old. She sees her once a week, when MIL comes to our house to care for DD1. (She would like to be caring for both children, but DD2 generally won't last with her for more than 15 minutes at a time.)
DD2 is very different from DD1 in this way -- DD1 was perfectly happy to be held and cared for by a wide variety of people, and was since I work part-time and when she was a baby, I cobbled together childcare from many relatives and neighbors. On the other hand, nearly from birth, DD2 has protested strongly when she's held by people other than her parents. She's gradually broadened her "acceptable" category, so that by 3-5 months she's often been willing to be held by friends and relatives she's never met before, even for long periods of time. But MIL, who she sees frequently and is held by regularly, continues to be in the category of people she won't tolerate for long. MIL thinks this is because I wore DD2 more hours per day than I wore DD1, and because when she was little she slept closer to me in bed (I co-slept with DD1, too, but not "snuggled").
DD2 is perfectly willing to sit in my lap and look at MIL. We do that for a long time every week. But it doesn't seem to be helping her be ready to be cared for by MIL. I guess we all thought that after doing that every week for almost 6 months, we'd have made more progress.
And it's a problem because I do work, and I do need childcare, and MIL is our primary childcare provider, and DD2 has a harder time with her than with most people, and MIL blames me.