Depends on the nature of your job, and the personalities of your children, I would think, as well as your own personality. Most people cope best when they have balance between both work and childcare.
I'd take a day of playing with my children over my job any day. However, I would prefer working than arguing with my kids about cleaning up after themselves and doing their homework.
As for stress leave, there are two extremes that could be happening. Yes, someone could go on a manufactured 'stress leave' not because they are experiencing unmanageable stress, but to give them a reduction in income and more time to prep for court. But family court IS very stressful and hard to deal with, and taking time away from work helps.
I suppose you could argue that the reduction in income is temporary and the person should be imputed to their full income, because if they took the stress leave due to the pressure of family court, once the trial is over, the stress should be gone and they can return to work.
What is your ex's job? Is it paid stress leave? How is he supporting himself?
In your specific case, time to remind your ex that 50-50 would involve less financial strain to him due to the offset system. And yes, if he's off work, he's perfectly able to care for the children while you work, and save you both daycare costs.
If he doesn't want 50-50, a judge is going to tell him he's got to pay table CS. If he doesn't want to care for the kids or pay CS either, I imagine that thought could be stressful.