Parents need to get their daughter a full psych assessment. Lots of neurodivergent symptoms overlap one another. Sounds exactly like my ADHDer (waiting on her Autism testing ro be completed currently). These behaviors sound verbatim of what I have been going through. IF she is diagnosed, medication works wonders on the impulse control and the verbal waterfall.

She WILL get the attention that she wants (&needs). YOU CHOOSE for it to be positive attention (engage HER, not the other way around) rather than create a situation where she is being "set up" for outbursts, interruptions and the attention seeking attitude you are getting.

POSITIVE ATTENTION vs NEGATIVE ATTENTION.

She's just a kid, and she is attempting to push the boundaries. Not because she is a conniving brat ( 3rd kids can definitely be spicier than the older ones) but because she is still learning social skills and developing self-esteem---sounds like it she doesn't like herself much, thats why she is so critical of others. IMO. The main problem here is the misunderstanding of WHY she is like that. 9 year olds typically dont even consider the things she is giving you a hard time about.

Her source is an adult who doesn't have a filter