I agree that this isn't normal, but Cicero has a point (page 1)
When my youngest was born one family member believed she was great with babies and admittedly was a nanny when they were younger. But due to many medical issues the person was barely able to stand up without assistance and at the time needed a wheelchair but refused to use it. This person gave me a homemaid coupon book saying they would babysit, and made it very clear that they would be doing most of the holding of baby during family events. I didn't feel comfortable having this person hold the baby at all unless they were sitting on a couch with another adult sitting next to them. (like you would do with a young child holding a baby)
I asked a few key family members to watch and intercede when necessary. I know it made them look rude and pushy but it kept my child safe. A few months later she was hired at a daycare to watch babies and was fired during the first two hours once they figured out that she didn't have the ability to carry the babies, or even bend over to pick up a baby without falling down herself.
I am not saying that this is about you but it might be interesting to see if there is someone else in the family that might be causing such an intervention. Maybe a heavy smoker, someone who doesn't have immunizations during an epidemic, a closest drinker, etc