How can I stop my texts from going to my sisters iPad?

I'm guessing here that you are referring to texts that are intended for you, not ones you are sending her. It sounds like the two of you may be sharing an Apple ID (if you are STOP), or someone has configured a device to do text forwarding. On your iPhone, go to Settings>Messages>Text Message Forwarding, is her iPad selected?

if you meant imessage then stop sharing apple id for imessage.