Is it permissible to leave one fingernail covered with nail polish without removing it for wudu, under the pretext that Islamic law overlooks a small amount?

For ablution (wudu') to be valid, water must reach all parts of the ablution organs. Therefore, removing anything that prevents water from reaching the skin is obligatory. This includes nail polish (manicure), which prevents water from reaching the nail. This is not something that can be overlooked. The wife must repent to Allah and repeat the prayers she performed with an invalid ablution.