Claiming a dependent is not optional. Review the rules at this link for Who can I claim as my dependent?, to make your determination.
That being said, if your father claims your son as a dependent you will not get the stimulus. Only the person who claims a dependent is eligible even if the income is too high and they don't actually get any.
One of you will definitely be reviewed and only one of you is allowed to claim your son. Review the information to see who is the person that is actually eligible to claim your son. Only that person will be allowed.
As far as government assistance, you will need to check with your local government agency to find the answer about that.
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