Welcome. Don't worry, nothing is wrong. You have your own profile and your father is connected to you. What you now should do is to go to your own profile, edit and then on the right follow the link 'add mother'. On the top of that page, there is a small box for the profile ID. In there, you paste the ID of your mother.
That should add a link between her and you, and will also create a link between your father and her.
You can also go to your father and add as spouse there. Use that ID as well. Problem then is that you will probably not be seen as daughter, but as 'half'. So for now I would not suggest that.