Hi M.! I was invited to Mamasource, though I am not a mom. I'm an auntie and am very close with my nephews and nieces. From observing their moms and remembering how I was at your stepdaughter's age and what my owm mom has done with me, I feel like I can share my opinion with you.
First of all, it's not a bad idea that you posted. It will help you and give you different ideas. 13 is a hard year. It's the beginning of the teenage years. my goodness...I remember being 13 and being a monster, but that was a bit different!!! All 3 men in my life vanished and it was just me and mom. Yikes.
Enough about me! A problem I see is that you ground your daughter for a couple of days, then she's nice and gets off from being grounded. When I was younger and got in trouble with mom (she and I didn't have that great of a relationship when I was younger, but we have a better connection now), she would always threaten me twice, then actually do it and stick to it. Once you give in on the punishment time, no matter how good they are during the time, you shy away from the punishment. In a child's mind, they basically know how to wiesel their way out of punishment because they know what to do the next time they get in trouble, so no lesson is learned. I was avid in soccer, chorus and drama (to name a few). When I wouldn't do what I was suppose to do or do something dumb and got in grounded for it, all of my extra ciricular activities were taken away from me for a week or two, depending on the crime. She never backed down from where she stood, otherwise, my lesson would not have been learned. My senior year, I got into some trouble (we'll leave the "what happened out!!! lol). This was around my senior homecoming. Guess what happened?! 2 weeks beforehand, I got in trouble and was unable to attend it. She didn't back down, but I learned my lesson. Basically, stick to your guns. Make your children respect you otherwise it will just get worse as they grow older.
If it's anxiety and jealousy that she feels, I think you and her need to have your day together, without the other children or her father. Get your nails done, go shopping, whatever. Let her know that just because you have other children doesn't mean that she is loved less. At the same time, let her know that because she is the eldest, a lot more is expected of her. Explain to her that her younger siblings look up to her as a role model (which is the case) and that her younger siblings watch her every move and follow in her footsteps. That should help change her ways back to that sweet loving baby girl she once was. Also, when you have that one on one talk with your daughter, ask her if she would like to see a therapist. Let her know it's completely, 100% up to her. A therapist is a nuetral person who won't take sides, but just an ear to listen to what his/her patient has got to say. Maybe she just needs to vent? Just an idea...I'm not saying that she needs one, but who knows?! It could help her.
I commend you for being the time of mom who doesn't let her children walk all over her. Motherhood is a hard battle, so I've heard (and seen!!) but the outcome is precious and worth ever battlescar. You will do good. Realizing the problem is the first step to fixing the problem.
Good luck, M.! I'll pray for you!