Is it sinful to let my wife wear makeup outside in public on Eid?

So there's a couple of things for this. Number one, it depends on the nature of the makeup. If it is something that is not going to attract undue attention, it might be covering up blemishes for example or something which is mild, then that wouldn't necessarily be sinful for her and you would have no sin on you either. If let's say something which is the opposite which is going to be very attractive and attracting the attention in the vicinity or the presence of non-mahrams, then that's something that you as the husband need to then convey to her because it's your responsibility. You have to take care of your flock as the Prophet Sallallahu Alaihi Wasallam mentioned in the Hadith of Bukhari. So you would need to then have that discussion in an appropriate way of course as to the degree and the level of makeup in that particular context. Now if let's say the female goes ahead and continues with that with the level of degree of makeup which is attracting the attention of non-mahrams, then there would be an element of sin potentially on her but not on you because you've done your duty.