OP - I think you need to stop thinking about what your PIL are doing for your SIL, and think instead about what they are doing for DN. They clearly don't need to run round looking after your DC because if they don't do it, your DC won't go without/suffer, whereas, if they genuinely think your SIL can't look after her child by herself, then they might feel they need to do it for the child's sake, not her sake.
I would take it as a compliment to your obvious parenting skills that they aren't worried about the level of care your child gets.
As others have said, it reads like they have taken on a parenting role with DN, this might well be because they can clearly see if they don't do it, no one will, and in order to be put up for adoption in the first place in this country, that child has already suffered in their life, they probably just aren't prepared to watch that child suffer further.
Allow them to be just grandparents to your child, not extra parents. You don't need that do you? You are capable? then you don't need to play these silly games with SIL.
Perhaps stop looking at her as 'competition' and start pitying her, for her to come out with crap like that, then she is clearly not an emotionally strong person. She must have fought to adopt a child on her own, how sad to have gone through all that and then not be able to cope with the reality.