T.C.
Tape it on with packing tape or duct tape. Some kids are ready to potty train at this age (especially girls) and going diaperless is one of the best ways to teach it. BUT the fact she's peeing around the house makes it seem like she's not ready. I wouldn't allow having the diaper off be a choice for her to make. Duct tape it on if you have to. She'll probably be really angry at first, but she'll adjust.
She sounds similar to my daughter. She knows exactly what she wants and how she wants to do it and if she doesn't get her way she SCREAMS and is a little drama queen. My son was so easy compared to her. My other daughter was also much easier. Some kids are much more challenging than others! But be consistent. If you're not okay with it, then don't allow it. Try to approach it from a positive parenting point of view instead of punishments, as I find this ends up being a way that causes the least amount of upset. Good luck!