What is the ruling on taking money from a maternal aunt who has ample wealth and claims not to, for the purpose of spending on her daughter and grandchildren, whom the questioner supports and is in need?

Your wealthy maternal aunt is not obligated to be supported by you, because one of the conditions for the obligation of support upon a relative is that the supported person must not possess wealth or income. And your maternal aunt's daughter is not obligated to be supported by you or by your mother, because the support of a relative, other than ascendants and descendants, is not obligatory except upon a relative who is an heir by fard (fixed share) or ta'sib (residuary).

It is not permissible to take from the aunt's money except for those whose support is obligatory upon her, should she refuse to pay. If the support for her daughter became obligatory upon her mother, then her daughter (or her representative) may take from the mother's money the amount of the obligatory support, even without the mother's knowledge.

Your taking from the aunt's money without her knowledge, in return for what you spent on her and her daughter, is absolutely impermissible. However, if the support for the aunt's daughter and her children became obligatory upon the aunt and she refused, and you intended, at the time of spending, to claim it back from her, then you have the right to demand from her what you spent.