The situation you are facing is, unfortunately, all two common with “blended” families such as yours. Your father had two sets of children, one from each of his marriages, but
he has given legal authority to the children from his second marriage, through the powers of attorney that you describe.
From a legal perspective, the key questions are: (1) are your step-siblings acting within their legal authority granted to them by the powers of attorney; and (2) are they violating their broader responsibilities with regard to the personal care or financial management of your father. The first question can be answered by reviewing the powers of attorney – and unfortunately, if they refuse to share those with you, you may need to file a lawsuit against them to challenge their actions and thus have the opportunity to review the powers of attorney. The second question involves the option of seeking a conservatorship over your father – where one of you (or a professional fiduciary) would be appointed to manage your father’s affairs.
Generally speaking, your step-children have the legal “right” to do what they are doing – but that right is subject to a review by a court. Each state has its own procedures for this review, and its own standards for evaluating the conduct of an attorney-in-fact. We suggest that you have this situation reviewed by an attorney who has handled similar sorts of issues, and who can compare what they are doing to the local standards that a court will apply in reviewing the claim. That same attorney can also advise you as to the cost of pursuing legal action, and the likelihood of success.
But apart from the legal pathway, we think you should definitely explore less formal paths to resolution. We think you should start with the premise that your step-siblings care about your father, and explore why they have such a different approach to his care than you think is appropriate. If you approach the communication with this attitude, they will hopefully be able to explain their reasoning to you. Then, if some modicum of open communication can be developed, hopefully you can work cooperatively on the expenses and living situation for your dad. The financial and practical care problems are only going to get more complicated as he ages, and so it would be wonderful if you could make some progress in setting a new tone for the interaction now.