It sounds like the problem is coming from her Moms house, the lack of nurturing would have an effect on her needing more from you and her Dad,He does do plenty with her from your description,and yes the bad mouthing would make her worse with you. She is Nine have you or asked her Dad maybe to talk to her and say it makes you both unhappy to have her behaving like this, and ask her Why she does, as she is living at the other house it may be something you"ll have to put up with and hope it changes as she gets older, the Problem more than likely is in the other Home.Try not to react to her as they do like to provoke to get attention.
We are both very involved with her. My husband and I share all the duties. He has been such a wonderful father. He even brushes her hair and puts it in a pony tail, takes her to the park, takes her to church. We tuck her in every night, read stories etc. We keep her in a routine because tht seems to make things easier for her. At her full-time house things are pretty unorganized and very out of control in my opinion. Bio-mom is not very nurturing. Mom bath mouths us to the kids a lot. She does this same behavior at her mom's house. Her mom gives in out of frustration. Bio-mom will not communicate with us well. SD is in counseling. This morning was really bad. I was late for work. Frustrated.
Sounds like her way of getting attention, she probably has found that negative attention is better than none, try not to react when she says and does these thingm its hard but if she shouts and Bad mouths you all, let it go ,walk away ,perhaps if she gets no reaction from you she'll give up.Have you had a talk with her and asked her why she is feeling like this,there sounds like there is a reason,, The complaining you just let go dont say a word about it, or you get into a battle The spider stuff well a lot of children and adults are afraid so that you should be okay with.Is she the same at her other Home? she could be feeling left out with her Dad ,do you all do plenty of activitys together where she is feeling Happy, and Busy.