I accidentally erased a longer reply, so this will be quick, but my bottom line was that you need to have her tested for an expressive language disorder. My son had some fine motor issues, but learning to type (which he did) wouldn't have solved his writing issues. He needed a lot of specialized help, but putting him in a low reading group would have just made him feel awful, be bored, and lose interest. He had an IEP from 3rd grade (when it was diagnosed) through 7th, for speech and expressive language (he had one previously, but not for expressive language) and although his writing has improved, it has never reached the level of his reading. This summer, as he was doing the summer work for his freshman honors English and AP World History classes, it was painful to watch him writing (soooo slow, and at times really struggling to make his point), BUT - even if he struggles a bit with the writing aspect, I know he is in the right level classes. This is a kid who already has a 34 in ACT reading, so I know he can do it, he just can't always express it. He would be bored out of his mind in a regular-level history or English.
I think it's ridiculous for the teacher to place her in a reading group based on her writing. If this is something your school will do going forward, I'd definitely look into testing her for expressive language issues or fine motor issues, and I'd also look into out-of-level testing so you can show just how advanced she is with reading and advocate for her to be put into a group at the right level.
BTW, my son was always, always in the highest reading group/gifted classes, and his writing didn't hinder guided reading in any way - if there was group writing, he wasn't usually chosen to do it :)- but he did just fine.