10 Gallon Tank Divider not working?

I have two male bettas in a 10gal tank with a tank divider from Petsmart. The side with the filter on it has clean, circulating water, while the other one's water is completely still and has a layer of slimy stuff on top. That particular side has my betta that has been suffering from fin rot, so he has more of a need for clean water; I switched them this morning so he'll have cleaner water. However, the other one can't lkive in that water either. Can I just punch holes in the divider? The dirty side right now is pretty much a bowl with no filter or circulation!