My son was such a clingy baby and he refused to accept anyone but me! Because I had to go back to work soon and my mum would be caring for him when I am away, I started getting my mum more involve with him whenever I can e.g. during diaper change, distracting him while I eat, bath him while I'm around, etc.
It took him about a week, and I left him alone with her for about 2-3 hours at alternate days to sleep (lol) so that he would get familiarize with her.
Thankfully, by the time I started going back to work, there was no drama crying... in fact he seemed pretty happy that I was leaving!