I don't know much about this (I used to post here lots and have a DD with a structural brain malformation plus two others, one of whom I think has ASD) but I would say you're in the same position I was in when DD2 was 6. She's now 9.
You know there is something. They know there is something. But you don't agree on a) what that something is and (possibly) b) the extent/seriousness/longevity of that something. The way I see it, you have two choices:
A: It's ASD and you know it's ASD. ASD isn't going away - ever. So it doesn't matter if they spend a bit of time thinking it's trauma and doing art therapy with your DD, because 1. It may help a bit but the ASD will still be there and then they'll have to deal with it or 2. It won't help at all and the ASD will still be there and then they'll have to deal with it. You're playing the long game.
B: It's ASD and you know it's ASD and they're going to flaming well get on and admit it.
A will involve thanking them for their considered view, consenting to art therapy, with the caveat that you still have concerns re. the ASD presentation.
B will involve asking for another opinion, etc.
I went with the A approach because DD2 was so anxious that nurture groups couldn't harm her and professionals just weren't prepared to look at her with an ASD hat on, I didn't have the money to go private and I was too battered to get arsey. Now that she's 9 and in year 5, I'm being encouraged to seek assessment and school are willing to back me with professionals because none of her difficulties have gone anywhere and they just stick out more.