I agree with Alan, i tried putting my swordtail into a breeding trap for her first lot of fry, she hated it and wouldn't release.
Imagine how your missus would feel being put in a small closet and told to give birth, you would want her as happy and comfortable as possible, same goes for fish.
Mine are in a 4' tank with heaps of guppies and good plant cover and they breed fine, i've found you can leave the parents and young together as long as you don't let the parents get hungry or bye bye fry.
As Alan said you'll run out of tank space so it is best to have another tank, there's nothing worse than needing one for a sick fish and not having one, by the time it's cycled ready for a sick fish the sick fish will be a dead fish. (found this out the hard way)