Edited to say: The site didn't give me an option of looking at what other advice you already had, so my info is basically redundant, but I'll leave it anyway.
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Having worked for doctors for 20 years, I would say you need a little info to help you understand the NP's side of things.
In medical billing, they have specific phrases that do not necessarily match what you'd say in regular English. When a child is not gaining weight as they should, there isn't a code that says "not growing much" - so they have to use a technical term - which is "failure to thrive." That does not in any way mean you are doing anything wrong, it is just the lingo docs, other providers, and insurance companies use to understand each other. There is another code, I believe it is inadequate weight gain? But I can't remember right this minute. It is not a judgement, it is a description, and it is required for the provider and the lab to bill your insurance company.
As for her asking whether she is sure the babysitter is feeding her - I would consider that a completely appropriate question. The NP is not there to tickle your ears with only the most polite of questions - she is using any idea she can come up with for why your daughter is not doing as well as she could. Once my daughter was having a problem, I can't even remember what it was now since it was at least 10 years ago, but the pediatrician asked whether I thought someone might be getting to her - it was clear he meant is there any possibility she was being molested or something. I said no, there was no chance of that. I was not offended - it was his job to consider every possibility. Me saying no was good enough for him.
If you take a defensive posture, it will be noticed and possibly documented in the baby's record. If you don't get along with a provider, that's not a big deal, happens all the time. Its not a problem to request a new provider at the practice, just say something like "I think her style is just not clicking with mine."
We are the momma bears, protecting our cubs for anyone or anything that might hurt them - but in this particular case, I think a little understanding of the NP's frame of mind might help you feel more at ease. I would definitely suggest changing providers so things don't get worse, but try not to be angry at her for asking important questions, and using lingo that providers need to use.