I know it's not supposed to be realistic, but a kid talking about getting a lawyer ?
In the webnovel it was explained that the teacher (the one that become Yuki's neighbor) dumbfounded by his statement as well, no normal 4th grader would saying calling a lawyer without making it a joke.
But the thing is, Yukito isn't a normal child, Kokonoe family just have that good of a genetic, Yukito were actually just like his older sister & his mom who is academically gifted, hence why he often draws jealousy from his peers. When his mom & sister didn't trust him and both teachers dismiss his claim easily, Yukito then contacting the next most reliable adult he knows which is his aunt Yurika, that's where he got advice on to questions every adult in school for a testimony, and since Yukito in factually never touched the hand mirror, there would be none of his fingerprints on them , only the actual thief, that's why his aunt SERIOUSLY prepared him a lawyer, Yurika knows how much a problem magnét her nephew is, she went this far because she knows better than anyone that for Yukito who has track record of almost losing his life due to false accusations, they need to go this far in resolving the problem, otherwise the issue will bite back at him in some way or another.
So yeah, just the details from the WN that they ommited on the Manga.