I can not answer your question because I do not know what "the family trust account left by your father" is, or what the terms of that trust document are.
Whether the trustee can legally distributed money to trust beneficiaries from a trust created by a person who is still alive depends entirely on what the trust document provides.
To the extent I understand you. your father's and your family's situation, it seems it might be sensible to distributed funds to needy siblings now. But as trustee you have legal, "Fiduciary" duties to carry out the terms of the trust. If you don't you could be liable for damages if anyone later complains (files suit) that you improperly handled the trust.
If you want to explore distributing trust money now, I think you need to consult a lawyer with good knowledge of trust law in your father's state. Have the lawyer review the trust document and give an opinion on whether distributions now would be legal.