Is it lawful for someone to work in childcare after voluntarily admission to a mental hospital for stress disorder?

Probably: You will have to disclose all medical and psychiatric problems with any employer. An admission for stress is not by itself a reason not to get hired. Check with your doctor and see if they can give you a letter saying you have been treated and what for. Good luck.

That depends: Having emotional issues does not automatic render someone as incapable of caring for children. However, one does require some degree of emotional stability. See what your contract says in regards to reporting requirements.