You can't gift Gold RUs so that is out of the equation. But let's say you could - what would the priority be? I recently had this issue come up (except it was gifting GE RUs which obviously is OK).

I believe it would've been cleared at your level as you're on the same PNR. When you receive a RU, it gets cleared at YOUR level, not the giftees, UNLESS you are on the same PNR. Since you aren't on the same PNR as your mother, it would be cleared at the highest level of you/your wife as you either get upgraded together or rejected together unless I'm mistaken.

If they are cleared individually then yours would be assessed at GE, i.e. at the very top of the upgrade chain, and your wife would be assessed at Jade, which is at the VERY BOTTOM of the upgrade chain (my Air NZ rep said Jade RUs cleared below OneUps but that is controversial on here).

However, APD's are ALWAYS assessed at GE level, no matter the status of the person receiving it, which is also above Gold RUs. I'd much rather upgrade a relative with no status an APD upgrade since it's far more likely to clear that gifting them one of my RUs.