Which is correct, "我对我的妈妈说很多话" or "我对我的妈妈说很多"?
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.