I don't know anything about Nepenthes (Pitcher Plant) but there are quite a few listed in the database. Hopefully someone that grows this interesting plant will pop in and offer advice.
I agree that your mom's droopy plant is a Peace Lily and they love water! Mine that are planted in soil will completely flop and get real droopy when I forget to water them but they perk right back up after a good soaking. A couple of months ago I divided a really crowded peace lily, washed all soil from the roots and put them in glass vases with pebbles and water ... so far they are doing great growing in water.