Is it permissible to use 20% of profits designated for charity to treat a child suffering from autism, if no private funds are available?

If the matter did not go beyond the intention and resolve to give charity, or expressing the intention verbally without intending a vow or uttering it, then there is no harm in spending the money on the son's treatment. A vow is not concluded by intention alone without utterance, nor by a word that does not imply commitment. Even with a concluded vow, if it conflicts with repaying a debt or a mandatory expenditure, the emergent right takes precedence, then one fulfills what they can of the vow, and expiates for the remainder with an oath's expiation (kaffarat yamin).