According to her I should have no input in schooling, discipline, diet, well being, extra curricular activities, anything.
To be fair, my biggest worry when my ex informed me that he was in a serious relationship was that she would consider to have a right of say in how our children was brought up. Of course, it wouldn't have been an issue if we agreed on everything, but it would have been a problem if she thought had a right to have an input on the above. Thankfully, despite some issues, she never felt this was the case.
When parents are separated, it's hard enough to come up with compromises to agree on the above. Usually, before the couple would have gone ahead to have children or to separate, a common view of how the children would be brought up was set. Of course this involves with time, hence requiring communication and compromises, but the last thing that is going to help with this is a SP thinking that they have a right to be a third party to this, if it is going to involve challenging these compromises.
Let your SD parents agree on how their DD should be brought up and focus on yours. How would you feel if for instance, your kids childcare worker were to tell you that they wanted to come to your house to check what diet they were on at home, what time they go to bed, if they are being given time out properly? You would tell them that this is between your husband and you and nothing to do with them, despite the fact that (assuming they go to daycare) they might be spending more time with your kids then you spend with your SD.
As for contacting you directly, I expect it was because communication became impossible between her and your OH and she hoped that it would be easier to do so with you. That wouldn't have meant her being happy with you making decisions about her DD, only to be a go in between. This only works if indeed, that person only relays messages, not take over for the other parent.