Yes, a bigger tank would certainly make them happier... but keeping them in that tank would mean water changes every other day, and tap/distilled water doesn't matter as long as you've conditioned it... (I always put a bit of conditioner in distilled water just in case).
Heat is definitely a big one though. Bettas are not coldwater fish, and therefore need heaters. You can buy 1 gallon heaters at most pet-stores.
IMO, it would really just be easier to keep them in seperate heated 2 gallon tanks, but that's completely your choice.
And I usually only let my bettas flare at mirrors for a maximum of five minutes... too much flaring can cause split fins and make the betta stressed/tired...