We went to visit PIL when DD was 2 days old. MIL "offered" to take DD out around the block (to show off to neighbours) when DH and I were getting ready to take the dog for a walk. My face must have dropped, as before I could even react DH firmly told MIL that DD was coming on the walk with us, picked up the wrap sling and tied it around himself.
The boundary was set in place there and then, and MIL hasn't been a a problem since.
DD is 15 months now and last time we visited, MIL asked if we were leaving DD, who was happily playing in the garden, there whilst DH and I took the dog for a walk, I replied that I hadn't even thought about it, but yeah sure, why not? DD had a great time (as she is through the worst of the separation anxiety and ready to be left), MIL had a great time, as she just played with DD and didn't have to console her, and DH and I had a great time as we were both totally relaxed about the situation, and the dog had a great time because he always does!!
As others have already said... DD won't be staying away from me or DH overnight until she is able to understand the situation, communicate her wishes, and get something positive for herself out of the experience.