Thank you so much for this information! Very welcome.
In regards to "constructive grandparent relationship"; initially, we did involve them in our child's life as 'grandparents'. However, upon several occasions they have endangered his emotional and physical well-being. You will probably want to research caselaw on this potential theory, as in, does your local court allow such a stretch. And I take it you are saying you referenced them as "grandma" etc? If a court will recognize "constructive" relationship, that invitation to her to be the grandma would be in her favor, obviously, but the fact that you believe and took action on her endangering his well-being, in both emotional and physical ways, would likely take a bigger role.
For example, they did not follow the pediatrician's advice of how to care for him when they baby sat and we were at work. Due to their refusal of taking his temperature and giving the medications as doctor ordered, his temperature got up to 104.7! OK, so you may be able to further request (if visitation were granted) that it be SUPERVISED, since she may be incompetent mentally to handle a the care of a little one.
Further, they violated the diet plan the pediatrician stated to us, we had informed them of this, and as a result the child experience alot of stomach pain. What ignorant people. If you have proof of this (such as a doctor record, perhaps you called the doctor about it, etc., retain that proof).
Both of these things endangered the child's well-being and we no longer allowed them to babysit. Understood!
Further, they have repeatedly involved themselves in visitation with the birth parents. I'm not sure the pertinence here - they are related to one of the birth parents? And they visited with these relatives?
Their names were nowhere on any of the court documentation and they were angered that we drew that boundary of not getting involved in the visitation/custody; In WHAT visitation custody? Are you saying the bio parents visited with the baby when you were the guardian?
this is after they have scheduled 3 visitations for the birth father without our permission or knowledge of. OK, I think you are saying that when they were babysitting, they'd invite the bio dad over, and or the bio mom?
Finally, they both repeatedly criticized our parenting in front of the child (from how we brush his teeth, change his diaper, what we feed him, the clothes we buy him, etc.) OK, that can be big - a bit of parental alienation. I can't stand it when my relatives chime in, it is insulting and gets them no where nice.
They have no criminal history. However, they do have a 38 year old son still residing in their home who is very dependent upon them and due to his behavior; we feel it is not safe for our child to be around him. Why?
Further, that speaks volumes about their parenting abilities as well. Not always, but would likely depend on the specifics.
In regards to "time-sharing or visitation arrangements that were in place prior to filing of the petition", there were no regularly scheduled visitations with them ever. Good!
However, we did offer them to visit at our house under our supervision due to their past behavior of endangering the child's emotional/physical well-being, to which they refused. This may be good - you were willing to allow them visits and they did not care enough about seeing the child to take what they could get, they'd rather have nothing.
They began demanding visitation unsupervised and/or at daycare. We disagreed with both and again offered them visitation at our house. Do you have emails or other documentation to these communications?
No petition currently in place, but the threat has been made for one to occur. We will not know until after the mediation occurs. Is this a private mediation you both have agreed to? Since there is no court involvement?