So sorry for your troubles! Unfortunately, a lot of pet stores misinform people, making fish care seem like a much smaller deal than it is. This means that a lot of fish live in poor conditions, and their owners don't realize all the fun they're missing out on if they had a healthy fish! Let me start off with a few recommendations:
-Bettas do best in 78-80 degree temperatures, and a tank with a filter, so I would recommend keeping them both in a tank with a filter & heater year round. They will live much longer, and be much less susceptible to illness.
-I'd recommend getting a new tank, or a second tank for the other fish, 2.5 gallons is really too small for two fish. The rule most fish keepers use is 1 inch per gallon. Both bettas grow to be 2.5 inches long, so you should have at least 5 gallons for them, although a 10 gallon would be better. If you wanted to separate a 10 gallon, you could get something like this: http://www.aquacave.com/detail.aspx?ID=1557#
-Bettas can really stress themselves out by being able to see another one, they will display regularly, which tires them out. It's probably best for you to have a setup that prevents them from seeing each other (or their reflection)
As for repairing the divider, I'm not sure what can be done for that, as it's not a standard tank size, so there aren't 3rd party dividers on the market. I'm glad that no real damage has been done to either fish, and you did the right thing in separating him until a permanent solution could be found. Feel free to ask if you have any further questions!