How can I make certain that my dad's financial assets are protected?

The people who need to see the POA are the people she is interacting with on your dad's behalf. For example, if she is in contact with an insurance company about one of his policies, they will want to see the document.

I'd make copies and hand them out to anyone interested, but that is not required. Children have no inherent right to see it unless Dad wants it shown to them.

In what way is your father incapacitated? Did he need care before he was hospitalized? Who provided it?

If your dad is content to have his funds used for his sweetheart's benefit, there really isn't much you can do about it. If he has been supporting her and her family for four years, he may want to continue to do that. If she has been paying her way, through any income she may have, including child support from a former spouse, etc., then presumably she can continue to pay her own way.

What is the medical prognosis for when father will leave the hospital?

Not sure about your right to see the POA documentation - annoyingly enough, the information about who in the family has the right to be informed about it would be on the document itself, assuming it exists - but if she's collecting his social security payments on his behalf then social services will want to see it. Even then, they may not be able to talk to you about it; but you should be able to get them to sit up and take notice.

I personally would guess that she has no such document. If you were being confronted by your partner's children demanding to see it and you had it, duly signed and sealed, wouldn't you give them a copy each, perhaps shoved where the sun don't shine? But she may just be digging her heels in on principle.

When you say your father is incapacitated and in hospital, do you mean that he is physically unable to act for himself, or mentally? Is he of sound mind? Because if he is of sound mind, and he's perfectly happy for his girlfriend to operate his accounts as she pleases, you can't intervene.

Forgive me but I'm bound to wonder: is this really about justice for dad or is it about you loathing his girlfriend and her brood? It might be a better idea to focus for now more on your father's wishes and his recovery, God willing, and less on your suspicions about what missy is up to.