Your 12 year old will have had enough one day, and stand up for herself. Maybe ask your husband to talk to the 13 year old and ask her why she's so adamant about being so stink in bossy... I'm sure there's a mommy issue there, and it really has nothing to do with your 12 year old.
Bring them back to elementary level. Write on the calendar who gets the from seat which week, who gets the last shower, etc... or just ignore it. Let them hash it out for themselves, and stop playing referee. Bluntly say 'I don't care, you two settle it'... and eventually they will, because they're not getting the rise out of you that they'd like.
Hate to say it, but the 13 year old should know better. There's something else going on there. It's not about the damn remote control ;)
My brother and I are 21 months apart, I'm older... we STILL argue about silly stuff, but my mom told us a long time ago she wasn't playing sides, and we always had to hash it out on our own... and we did!!