Hi and welcome,
Cazza has made a good point, - also, some pups just don‘t particularly like being picked up, my dog wasn‘t overly fond, I remember picking him up rather clumsily when he was very small and held him under his tummy which undoubtedly hurt him because he squealed like a piglet! After that, I made sure to always support his bottom.
Your pup might also sense your wife‘s nervousness a bit too, the more she can learn to relax and interact in in a fun way, the quicker their confidence in each other will grow.