This isn't exactly an answer to your question, but it is kinda related....
My son had shoulder dystocia and some *minor* birth trauma - to his neck, right shoulder and right arm. His head DRAMATICALLY tilted/flopped to teh right, and his right arm had a "lag" in comparison to the left.....The medical professions said it was "just" an inflammed nerve and that nothing could be done about it, maybe some physical therapy in teh future if the lag presented any sort of "problems" - Hello, the lag is a problem, isn't it?!
At a month old, I took DS to the chiropractor and thank goodness I did!! The top vertebrae, the one the head sits on and pivots on to look around - was dramatically out of place, tilted out and sideways!!! Made so much sense as to why his head was so tilted, why his arm didn't work right, why he hated nursing if he was laying on that side.... After teh first adjustment - WOW what adifference! He was happier, nursed on that side, and was turning his head around. He was even moving his arm normally!
Of course teh medical doctors NEVER picked up on the trauma to his neck (despite doing Xrays on his neck/shoulders afre birth) - just the lag with his arm - *I* had to point out the funny floppy head thing he had going on, of course to be told nothing was wrong....
I REALLY encourage you to take your little one to see a family chiropractor - everything is moving as they grow, and it is SOOOO important to have those bones in the proper places as they are growing and muscles are developing.
And honestly, I would be really careful about letting your 3 yrold hold/pickup the baby - while I am sure your baby is PERFECTLY FINE I don't think *I* would personally allow it. Holding while sitting on the couch, propped up by pillows is one thing but picking up is quite another! There isn't any support for the baby's fragile neck muscles, and there is a possiblity that the baby coiuld be dropped. My nieces are 8 and 9 and they still have to sit on the couch to hold my son....My SIL did the same thing when the youngest was born (who is almost 3 now)