this all sounds terribly familiar. Card swapping, suspected pressure put on swapper, lost cards...At least you have an advantage, www, you are friends with the parents of both boys.
As this is the case, I think you could have a word with the dad. As you say, he did tell your son he could have the card back,and his own son heard him say it, so no excuses.
It's very possible his own son actually has the card still, but just doesn't want to part with it - the Yu gi ho obsession does strange things to boys IME. That's especially why I think it's worth asking the dad, if you son can't sort this out with the boy.
IME sometimes boys really want to hold on to certain cards, can't imagine life without them. It's amazing how many cards are 'lost' when the original owner wants them back.
My oldest son lost lots of pokemon cards that way - he'd show them to boys he didn't know well, (at playclubs or when he played out) someone would take his pack, show lots of interest, look through them, and lo and behold, his best cards were gone when he checked the pack later. I remember once going up to a group of older boys I didn't know, asking them if they had seen my son's missing pokemon cards as they were the last people to play with them, and being met with blank stares and head shaking
yes, it's a lesson leaned, and I had to do the same as you - tell my son he must not trade his good cards and keep a close check on who he plays with. He was far too trusting to begin with.
BTW - have you seen those amazingly cheap starter packs of Yu gi ho cards at boot sales and markets? Obviously copies, but very good ones - my sons are both very happy to get them. A starter pack (so 30 or 40 cards) costs £1.00. If you like, I can send you some.