The court works under the assumption that you as the parent, as you noted, have the absolute right to raise your child as you see fit, including deciding what family or other persons are allowed access to the child and what level. The burden isn't on you to prove that you should maintain that level of control and authority - rather, the burden is on grandma to prove to the court that NOT granting the petition would cause some harm to the child. That is a very high burden, and it's high on purpose. The court already knows these things. Grandma is going to have to provide a HIGH level of evidence to the court that there has been an extensive and ongoing relationship, akin to a primary relationship (ie close to living with grandma, not just visiting a few times a month) AND that your parental decision to exclude her can reasonably be anticipated to be detrimental to the child (either physically, emotionally, etc.).
What YOU want to bring to court is a list of exact examples like you've provided us above: what things has grandma done that show that not granting access is in the child's best interest? Your argument is that you want parental control maintained and grandma's petition denied because (a) grandma refuses to recognize your parental authority, (b) grandma refuses to follow rules that you've put in place for the child, and in fact prides herself in doing so, (c) grandma has attempted to coerce the child into denying your parental authority when she herself isn't around to do so, (d) grandma has age-inappropriate conversations with the child, (e) grandma is purposefully attempting to interfere in regards to your relationships by using the child as a tool of manipulation, and (f) whatever specific behavioral things you've noticed in regards to grandma "rubbing off" on your daughter.
That alone is likely to be all the defense you'll need. Grandma hasn't spent enough time with the child nor acted as a primary caregiver to the child to the extent that grandma's absence, in your opinion as the child's parent, would be problematic for the child - and certainly not to the extent to overcome the diverse types of negative impact that such contact would have, as listed above.Now mind you that she has never kept her every other weekend yet alone for more than 1 day. Over the past 9 mos it has been about 1 visit per month.
Remember, anyone can ASK the court for just about anything. Asking isn't the same as getting, and the court allowing the case to be heard shouldn't be taken as an endorsement that grandma has the upper hand because she's the one doing the asking. She's got to overcome the burden that you are automatically assumed to be a competent loving parent who has made decisions based on the child's best interest.

