I've slept in bed with my parents when I was young, when I was afraid and that hand on the private parts thing isn't normal. None of my parents did anything like that thankfully. That doesn't happen by accident or in sleep.
Always trust your instincts - I had a good friend when I was in high school whose father used to molest her. He did 'accidental' grazes all the time at first and by the time she was 15, he was raping her. Thankfully she was able to get out of that situation but these 'accidental' groping or grazing the private areas is total BS. And, women often have good instincts but the problem comes where women brush them off as being 'in their head'.
If you're not sure what's real or not then start writing things down. Any time he makes you feel uncomfortable, write the details & date down. It may help you see things clearly. Plus, if your father continues his behaviour or does in fact molest or rape you, the diary can be proof of behaviour to show your mother or police.
But if you know he IS molesting or raping you, then you need to go to the police. Molestors are NOT one time offenders. They always hurt more than one person. i.e.) My friend from high school, her father started raping & molesting her sister as well. & many molestors go after their child's friends as well. You don't want to discover one day that your father hurt one of your friends too, do you?
And to anyone who thinks this is 'in your head', ignore them. I've found that men (no offence) don't always see the inappropriate behaviour. Usually that's because it's done when they aren't around and therefore, they can't see how subtle these things can start out. Another friend of mine was molested by her babysitter when she was 8 and the sitter convinced her they were playing a game at first and then his hands were on her privates. She was too scared to tell her parents, then the next time he insisted on washing her because that's what her parents hired him for, so then he started molesting her in the bath.
Kids (and that includes 13 yr olds like yourself) are vulnerable and are made to feel guilty. That's a molester's MO/pattern because if the kid feels guilty then they'll want to please the molester and therefore be less likely to say 'no' to things (therefore allowing him to wash you, etc). It provides easier access to you and then he will take what he wants. Definitely not the kid's doing, but as they're innocent and vulnerable, the molester will exploit that and made them feel horrible even before they start molesting them.
This needs to be taken seriously. I urge you to keep a diary of weird or uncomfortable things you're noticing with your dad and to tell your mom. I know several women who were victimized when they were younger and it's caused serious trauma.
Besides, if something were to happen, it will help you cope, knowing that you tried everything you could to stop it.
No matter what you decide to do, if your father tries to hurt you, you do NOT deserve it. Even if you chose to do nothing, it isn't your fault. He's the adult, he knows what is appropriate or not & no matter what you wear or how you act, you're his daughter and he needs to treat you as such.
You must have these thoughts for a reason. It could be something as simple as waking up in the middle of the night, half asleep, to your father touching you. You may have thought it was a dream... it could be anything but if you feel it's a possibility then it may be true. Take it seriously. These thoughts aren't common unless they're based on something real.
***If he does try something, be vocal. Tell him 'no', kick, scream, fight. And as I was always taught, if a guy tries to hurt you, hurt him first. The elbow is one of the strongest parts of your body, elbow him in the face. Stick your thumbs in his eyes until he lets you go, claw, kick, scream & fight. Do what ya gotta do to get away. If you still can't get away, try to leave as much damage as possible to hurt him back & to try to get DNA samples so you can convict the bas***d!