I have been reading online on this subject and a lot of experts say that using nail polish, polish remover, "nail hardener", and chemicals damage your nails and make them weaker and prone to breakage. The best thing you can do, according to these experts, is to ingest the amount of calcium you should every day (according to your age), moisturise your hands, nails and cuticles, and eat healthy. There's no magic potion that will make them harder and stronger. All those products that claim they can, are not quite effective; in fact they make bigger damage. And I you wash the dished do it with some gloves on, the detergent and soap also dries them out.
Hope this was helpful