What would you call it when an aunt complains about her nephew in front of his mom to needle her?

Solution 1:

Passive aggressiveness is very apt. Provoking also comes to mind, depending on how we interpret her motives: she seems to be trying to provoke the child's mother, she is trying to get under her skin, she is trying to put her down. I am assuming that the mother of the child is her sister-in-law: she is trying to drive brother and sister apart by provoking the sister and setting her husband up against his sister by pushing him to join her in her provocations. She is a sower of discord, a bully, a manipulator. And, no, I have never had a sister-in-law perform such tricks of bullying and manipulation on me.

Solution 2:

To describe the aunt’s behaviour as “passive aggressive” smacks a little of pseudo-psychiatry.

More commonly one might say she is being snide:

adjective Derogatory or mocking in an indirect way: snide remarks about my mother

Solution 3:

I'd say it's a form of passive aggressiveness. She doesn't complain directly to the person she's complaining about--she complains to someone else in her presence. As you put it, "she can't be accused of starting a fight." That's one of the passive aggressive traits: Being argumentative or otherwise behaving badly, but with some kind of deniability built into the process so she can deny the aggressive behavior.

This is far from the only trait of passive aggressive behavior, but it is a type.

Solution 4:

I can't accept passive-aggressive as an answer (though I've not down-voted) because it does not mean "indirect complaints" (the behaviour you describe) but rather it means passive negativity, sometimes obstructionism, which is something else altogether.

I suggest this behaviour is better described as needling, where the aunt is goading and provocative. Needling is an informal word, but a good fit for this situation.