「パーティーの______[地震]{じしん}が[起]{お}こり、[会場]{かいじょう}は[大騒]{おおさわ}ぎになった。」
"An earthquake hit right in the middle of the party and the place just panicked."
While 「[最中]{さいちゅう}に」 may not be the only phrase that can correctly fill in the blank, it is a far better choice than 「うちに」. In fact, using 「うちに」 there would be highly inapproproate. Why?
When we say 「noun + の + うちに」, the duration of what that noun represents must be fairly long. It needs to last at least several days and it can last a few years as well. You might say:
「[夏休]{なつやす}みのうちに『ハムレット』を[読]{よ}むつもりです。」
It is fine to say that because the summer recess lasts 6 weeks.
Or you can place a whole mini-sentence in front of 「うちに」 to say something like:
「[日本]{にほん}に[住]{す}んでいるうちに、ぜひ[韓国]{かんこく}にも[行]{い}ってみたい。」
The speaker will be living in Japan for a year, so he can say this using 「うちに」.
To go back to the original sentence, we need to think about how long this party lasts. A few hours at the most, right? And how long does an earthquake last? A couple of minutes at the most, normally, yes? If so, that is your prime opportunity to use 「最中に」-- something quick happening right in the middle of a not-so-long-lasting event.
Regarding 「[間]{あいだ}に」 that you mentioned, it may not be totally incorrect to use it here, but it does not sound nearly as natural as when using
「最中に」. I will admit that some native speakers might actually use 「間に」 here, but to me at least, it would lack the "capture the moment" kind of impact that 「最中に」 gives you.