Is my prayer valid, or must I repeat it and my mother's prayer, after discovering a small paint spot on my hand after the prayer, knowing that I removed all the paint I saw before performing Wudu'?

If the paint spot does not prevent water from reaching the skin, then the ablution is valid and the prayer is correct. However, if it forms a barrier and prevents water from reaching the skin, and its removal is possible, then the ablution is not valid and the prayer must be repeated. Sheikh al-Islam Ibn Taymiyyah holds the view of excusing a slight barrier, but the safer opinion is the first one. As for your mother's prayer, it is not invalid because she was unaware of the reason that invalidated your prayer.