It appears the child has a few functions to communicate about : request; protest; cessation and recurrence. She is communicating this using non verbal means at present. So she is a non speaking child using non verbal means of expression?
Augmentative means of communication could be introduced to support her current means: use of a core board for high interest activities. Use of a core and fringe board also.
Part of your role as an SLT would be to support the parent in having a conversation about initially ensuring a child’s means of communication is meeting lots of functions and working on speech production is not supporting that approach, at this stage.
The Means Reasons and Opportunties model is a helpful approach to work with parents on. It is understandable a parent will want you to work on a child’s speech but it is also our role to help a parent feel comfortable with the approach that introducing visuals as a way for the child to understand and also express herself should be explored first.
You would also be modelling through spoken means , the core words to support her reasons to communicate: more/again/stop/no/not/go/help/want. These are the words a child would say if they could to impact on their environment .
I have some information on the MRO model if you want to find out more? Anyway, that is the approach I would take based on the description of the child.