DD is eligible for 2x weekly in-school/pull-out speech/language therapy, but we also have put her in private speech sessions once per week.
Our insurance covers a limited number of sessions for children DD's age (7) but we feel she benefits from the combination of in-school and private therapy.
We pay a copay per visit ($25) plus anything that isn't covered by insurance to meet the deductible. (It appears that we have met the deductible on these kind of services already.)
My bother's sons also do private speech/OT sessions in addition to other accommodations through their schools. Both have IEPs on file; the elder one is on the autism spectrum and the younger one has a severe speech delay. My SIL was able to extend EI for a time for the younger one to fill the gap between speech-therapy preschool and "aging out", but she had to fight!
Once a formal diagnosis is in place, meeting with the school's child study/child development team (if they have one; this may depend on education provisions for children with disability classifications in your DGDs' home state and whether they are applied to nonpublic schools ... in a recent court case in NJ, they were found not to apply to religious schools) to see what resources are available is probably a good first step.
In the meantime, tell your DGDs' parents to check their insurance for the OT and speech-pathology/speech-language therapy coverage and to start calling any in-network specialists NOW to try to get appointments scheduled. (Don't be like me and call a few, get no responses, slack off, and then start up in 3 months.)
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Liz
DD (3/2010)
"Make mistakes! Get messy!" - Miss Frizzle