Is it permissible to clean the vulva with water and soap while bathing, then intend to perform ablution (wudu') and sprinkle water over the rest of the body without touching the vulva, with the intention that this bath serves as ablution, knowing that the vulva is not touched to avoid invalidating the ablution?

There are two types of ghusl (definition) (ritual bath): one to remove major ritual impurity (janabah (definition)) and one for cooling down. If the ghusl is to remove major ritual impurity and one intends to perform wudu (ablution) with it, or does not intend it, their minor ritual impurity is removed. However, if one intends to cool down or clean themselves, along with wudu, and they are not in a state of major ritual impurity, their wudu is valid if the washing of the limbs is done in the correct order. If one touches their private parts before washing the wudu limbs, their wudu is valid. But if they touch them after wudu or during its performance, wudu must be repeated.