Please don't listen to others about the tablet. In an more technological advanced and evolving world, it is fine for 9 year olds to have tablets, they must learn, keep up, and grow with a world that relies much on technology to maneuver and manage a lot of things.
It is also fine for her to communicate with her loved ones and the people whom love her as well via tablet within usage time. She doesn't need supervision to do this.
The adults should always inform one another and discuss the daughters request, and/or be able to flat out deny her and it be unanimous with all.
The problem seems to be poor communication and skills, perhaps built up tension, anger, and resentment, and perhaps intentionally/unintentionally weaponizing the child to lash out for old unhealed wounds from all or some of the adults involved.
You should always remain in communication with the grandmother, as she is actively involved in your daughter's life.
You cannot continue blaming the grandmother and say that she's intentionally undermining you, when she may be trusting her sons words as well as your daughters about things being okay. She may feel that you trust her father's judgement and you two are on the same page with coe-parenting.
You need to speak to her. You are a parent now. Whatever previous grudges you may have towards her perhaps when you and her son were together, work towards letting them go.
You also have to realize neither parent can have things their way all of the time, and things will be different at each house.
Focus on your 50%. You get breaks and days off. Your daughter returns..
If after speaking with the grandmother, if she still wants to get her a scooter for Christmas let her. Purchase safety equipment. It remains at grandmoms house. Discuss purchasing kid friendly ones.
Admit to them you're having difficulties with your daughter's attitude and mining your rules. They may get on board and tell her that if she doesn't behave for mommy and do well in school, there won't be any scooters or new things until she does.
In an ideal world everything would improve drastically and remain..
but... realistically,
If none of the adults ever come together,
Your daughter will always resent you and emotionally blackmail you eventually... perhaps eventually saying that she wants to live with grandma too . You'll remain an enemy and soon she'll start just figuring out how to get to grandmoms house on her own ..
The adults have to come together, or you may have to go along with a lot of things you don't approve of