Which is correct, "我对我的妈妈说很多话" or "我对我的妈妈说很多"? Can someone explain me which one is correct and why?
First, in Chinese if you don't want to emphasize "我的，你的，他的"，we usually remove "我的”，我对我妈说....or 我对妈妈说 is more natural.

Secondly, it should be added a complement "了" after the verb "说" to indicate the action is finished. So it could be 我对妈妈说了很多话。or 我对妈妈说了很多。

Finally, 说了很多话 means that you speak a lot "sentence" to your mother, while 说了很多 means you talk a lot topics or opions with your mother.