Hey. I don't think that's a good idea. When the male is guarding the nest, you'll want to not have the female near. He will get quite annoyed at constantly seeing her and thinking she'll be able to get to the eggs. (after a spawn the male usually forces the female away until you can take her out). Also, as the babies are growing you'll want to give them as much water as possible (and with frequent water changes too). Hormones and wastes from adult bettas can inhibit and affect the growth of the young betta fry so that's another bad factor for keeping either a female or male in the other half of the divided tank.
I'd say it's a much better idea overall to have a completely separate tank for spawning the bettas. Then you can take both parents out to their own tanks at the appropriate times.
Do you have any other questions I can help you with?