The only time a period/question/exclamation mark does not definitively end a sentence is when it is within a quote. The apostrophe would always come before the period. Your example would actually use "Jess's", due to how the word "Jess" is pronounced.

She was in Stacie's room, not the twins'.

Abbreviating a word such that it involves a period at the end of the sentence only keeps its period if the sentence ends in a question mark or exclamation point. If the sentence ends in a period, there is only one.

It was filled with candy, toys, noisemakers, etc.
It was filled with candy, toys, noisemakers, etc.?