Can my sibling, who is my father's POA, put the house in her name? Can she do it without his signature?

Hmm... it seems since you are the caregiver who lives there, they would want to transfer it to your name if at all. Real estate transfers before a will is executed can create many problems. You all need to decide what you want to do with the house after your father passes, then consult an attorney about the best way to do it so it doesn't jeopardize Medicaid eligibility if he needs it. Do you need to stay in the house after your father passes? If you have been there at least two years, your presence can help to protect the house from Medicaid recovery. Considering that, putting your sister or brother's name on the deed makes no sense to me. Where do you fit in here?

It can make it easier to avoid probate.

I have spoken to them. I believe they want to "put the house in their name(s) in order to make his estate easier and less costly to manage once he passes.

No. POA does not grant the right to transfer title to an asset to someone else unless it is in your father's financial best interests for such a transfer to take place, and it's hard to see how it could be; or unless they are acting in accordance with your father's wishes, while he is still capable of making such an important and complex decision (which would be pretty hard to establish, if the POA is already in force). POA certainly does not give your siblings the right to help themselves to your father's property. Could be they're trying to be too clever by half, and make your father look less wealthy than he actually is for some reason; but it won't wash, anyway.

Why are you worried that they might try to? Any concrete reason or just a vague dread?

They could, quite legitimately, BUY the house from him, if the aim were to release capital to pay for a nursing home, for example; but the sale would have to be at the market price. Have you tried talking to them about how they plan to manage your father's affairs?

If a POA uses their authority to transfer the house to their name, this is called a "Conflict of Interest" and any Judge would have a serious problem with the person who did it.

She can not unless your father has given her a power of Attorney over his financial matters. If he has a trust the home should be put in the name of the trust. If see has changed the deed to the house she now owns it. It sound like your sister and your brother have POA and that is a problem for you if they decide not to be fair.