When my DS was 8 months old we were in the same position - fed to sleep and had never been left with anyone other than short stints with DH. As he got older the length of time I could leave him with DH has increased and now I can leave them together all day. He is now 26 months old and yesterday I let him go to the neighbours when they were walking past and I followed 10 minutes later after I fed the baby. That is the first time that he has been in the care of anyone other than myself or DH.

So I don't think it is odd that you don't want to be parted from your baby.

As Raven said, take it as a compliment that your family wants to babysit. No one in my family has ever offered to look after DS, even when they knew that DH would have to miss the birth of our second child because we had no one to look after DS.