Might be a nice idiom to remember: "שמחה לאיד" - literally means happiness to a (-n other's) disaster/trouble. :)
Is that pronounced La'id? If so, it reminds me of the German verb "leiden" (to suffer) לאיד
It's שִׂמְחָה לְאֵיד With the niqqud, so I think it'd be something like "le-yd", instead of "la-yd" — I'm german though and I got this from a dictionary so idk
Would it be appropriate to utilize a contrasting conjunction for Vav? I.e. I am sad, but they are happy.
If you want to use a contrasting conjunction you can say "אני עצוב אבל הן שמחות" (but = "אבל").
Doesn't the vav conjunction also mean "but"? I thought this should mean, "I am sad but they are happy."
No. The meaning of vav conjunction is "and". If you want to say "I am sad and they are happy" use vav. Example: "אני עצוב והן שמחות". If you want to say "I am sad but they are happy" you need to use the word "אבל" instead of vav. Example: "אני עצוב אבל הן שמחות". (אבל = but)