Is this a formal exclusion and have you had official paperwork? Was DD's EHCP being followed at the time?
Funding isn't your concern. If the school haven't got enough they need to approach the LA. Your focus should be on ensuring all the provision DD needs is in the EHCP, and the provision is detailed, specific and quantified.
The outreach support needs to be in the EHCP. If it is then the support must be provided, if it isn't you can't force the school to provide it. If the outreach support isn't specified and quantified in the EHCP it is unlikely the school will receive funding for it.
Has DD been assessed by SALT, OT and a psychiatrist &/or clinical psychologist? Are the assessments up to date or do you need to request a reassessment of needs? Is SALT, OT, ELSA and some therapeutic MH provision included in the EHCP? Is a quiet space in the EHCP?
Unfortunately if the LA refuse your request for an early review you have no right of appeal. Your options are either wait for the AR or request a reassessment of needs which does come with the right of appeal if refused.
The school need to figure out why DD presents differently with others. Is it sensory overload? A different approach? A smaller class? The 1:1? Can DD communicate why she leaves the classroom?
Academic ability is of little use if your child can not function in everyday life. Mental health must always come first in my opinion.