Glad I could help. Your original question was about dividing so I focused on that without considering factors that can cause flowering issues. I should have added that peat does break down over time and can become anaerobic. You may want to repot your old sarracenia into fresh soil if they have been the same pots for over 3 years. A good way to tell if your soil has gone bad is if it smells nasty, like rotten eggs. If your sarracenia have multiple growth points but only producing one flower but otherwise look good, I would start with repotting into fresh soil in a bigger pot to see if that helps.
There are so many variables to consider when a sarracenia is not performing like it should such as soil conditions, climate conditions, water source, watering method, sun exposure (at least 6 hours of sun a day to look their best), and pest issues.