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Based on the information you have provided I believe both your son and granddaughter qualify to be claimed as dependents by you.
You need to provide more than 50% of their support. There is no dollar limitation. So receiving the disability does not appear to provide enough to prevent you from meeting that criteria.
They must live with you. And this is true.
So yes, you can claim them for the entire year.
Claiming them as dependents will not impact their future disability payments.