Do you have a fairly good relationship with both parents? I would try talking to them both (separately) and let them know that whatever the two of them are going through, you want to make your home and the time their dd spends there as normal and as consistent as possible. The dcg, should be able to have one "safe" place to be while her parents are dealing woth whatever they are going through. Talk to the mom and dad about how important it is for dd to arrive at a regular time and picked up as consistently as possible as well.
Tell the dcm, that if she doesn't arrive as scheduled she willbe assessed a late fee or early drop off fee. If she fails to call after a reasonable amount of time (like 15-30 minutes) tell her the space will not be available when she tried to drop off. Tell dcd, the same about late pick ups...if he arrives later than the scheduled pick up time, he will be assessed a fee.
It is hard to be stuck in the middle and probably even scary and very unsettling for the child as well. Which probably explains her aggression and unwanted behaviors. I would use examples of these behaviors when expaliaing to dcp's about the importance of consistency.
I would also tell mom to stop using words to the child and show her consistency and safety and security by keepong life as normal as possible right now. As far as the time outs, you can't make mom see the error in her ways (the TV and couch as time out ?!?!
) but you can definately offer some suggestions as far as how to properly implement a time out or "punishment" for behaviors at home.