"My younger sister also wants iced tea."
To me, 想 is more an expression of want or desire (or even longing, pining, or missing, as in 我很想你 / I miss you); whereas, 要 is more an expression of intention:
我想 ... = I would like ... (or "I want ...") 我要 ... = I'm going to (have) ... (or "I will have ..." or "I'll get ..." or "I will order a ...")
I would generally prefer to use 想, but maybe I would be wrong to do so, and I certainly would not think 要 is wrong here, either.
From what I read (after googling 想 vs 要), it seems 想 is more in line with a conditional form of want (but can be used to be polite), while 要 is more indicative form. Though, I would like to see if a native/fluent speaker could confirm this or not. My teacher always told me to use 想, but never really explained why (not enough time in three months).