I am the terrible sibling...

I would walk away from this, you will never please her, it is all there in front of you, your sister has showed you who she is...believe her. She has made her decision to take care of him, so now, she will pay the price of doing so. Boundaries are great IF they are enforced, unfortunately most do not and that becomes calling wolf and nothing more. Move on, you do not need the stress of trying to please another.

This is a difficult situation & I feel your pain with wanting to move or run far, far, far away. I think all caregivers feel that way sometimes, I know I sure do! The moon isn't far enough some days. Since you haven't had a relationship with your father for years, and you're suffering from anxiety & depression issues that are getting worse due to this particular stress, I would say step BACK and let sister-dear handle the mess SHE has gotten HERSELF into. If nothing you do is good enough anyway, what's the point in trying to help her? If she squawks at your decision, tell her you're under doctors orders to cut down on the stress in your life due to serious health issues. The end.
Best of luck!

Often well-meaning children take on caregiving without knowing what they are signing up for. One can never fully imagine how physically and emotionally strenuous (and financially) draining it can be. This is what your sister did and now she's in a pickle and thrashing around because she's probably burning out with no clear path forward. True, you didn't agree to the arrangement and true, you maybe did confuse her with how you expressed your offer of "help". Maybe time for a gentle discussion about how your dad's care is overwhelming both of you and maybe it's time that he goes somewhere that can give him the best care while preserving both of your sanity. It is just not realistic for a parent to expect their children to burn themselves out caring for them. It's selfish. Is your sister his durable power of attorney? If not this also needs to get taken care of sooner rather than later.

One last question: if you are involved because there may be an inheritance (and I'm not saying this as an accusation) then maybe it's time to give up this attachment and you will be very free to walk away. Wishing you the best in a tricky situation.

My first thought is whether you might consider speaking with a therapist or counselor for a session or two about this situation? It might help clarify things and help you get those boundaries in place.

My second thought is that you unintentionally confused your sister about what your role would be. You said you disagree with her plan, but would help as much you can -- and then you list all the ways you went beyond what was reasonable for your mental health, physical health, financial health etc., going along with her plan that you say you told her you disagree with.

I don't mean to be critical of you at all in this difficult situation, but your actions and words don't seem to agree and it may be confusing the heck out of your sister as well.

You have expressed that you never had any relationship with your father. He was, in fact, never really a father to you, other than a bad father. I for the life of me do not understand our wasting our care and love on someone, whether of our blood or not, who is clearly not worthy of it. If he was a good father to his other daughter then I am thankful for that. But he was not to you. So he is getting what he deserves, in my book, the love of the daughter who claims he was a wonderful Dad, and the NOT so much caring from the one he was NOT so good to. My question to you is to ask you why, for what earthly reason are you involved with them at all? Is there something you are wanting from him, such as saying "Gee, so sorry I missed your whole life"? Because you won't get it. Are you wanting something from your sister? Because you won't get it. You will be treated as the doormat that you have laid yourself down as. They are, in fact doing it right now. You don't need the permission of perfect strangers on this forum to do what is best for you in walking away. I would second the vote for your seeing a really good therapist to give you the courage to move away and the courage to understand that people who give you the label of "bad sibling" don't have a clue. They don't HAVE to have a clue. Only YOU have to have the deep understanding that you deserve a life, a life that neither of these two individuals will ever give to you. Your sister, or is it your 1/2 sister, made her own choice. I encourage you to make yours.

I think that you need to let your sister know that you are not able to help her as often as she would like.

I would put in writing what you are willing to do, what days monthly you are willing to do them. When she throws a fit, gently remind her that you didn't agree with the plan from the 1st and you have gone above and beyond and it is not sustainable.

Give her alternative solutions, lists of agencies, lists of facilities, housekeepers and then stick to your guns. This will probably get ugly before it gets over, but no one can make another person step up and do what they want done, she is unreasonable to request that you do caregiving because she decided. Nope, sorry, you chose this path and you have to figure it out and I am not your solution.

You can do this, hopefully your sister will see that he needs professional care and it is not worth fighting with her sister.

Hugs! What a crummy position to be put in.

you are NOT a terrible sibling. I recommend reading books on boundaries. This one helped me to feel less guilty and helped me to not believe guilt trips because it is written from a Christian perspective, why we must say no to others.
Boundaries: When to Say Yes, How to Say No to Take Control of Your Life by Henry Cloud (Author), John Townsend (Author) is a really good one. Also,

This one helped me to understand why I have trouble with boundaries given that I was raised in a home with very poor boundaries.
Boundaries: Where You End and I Begin - How to Recognize and Set Healthy Boundaries
by Anne Katherine

Run, don’t walk away from this. Take care of you, and be sure to remind her it was HER decision to move him in. And no guilt or sorrow. He and she chose their paths..... hugs to you..

I have a poor relationship with my mother. Had a great one with daddy. She resented and resents to this day that he and I were close.

It comes up in conversations and comments all the time. She cannot let it go.

A few weeks ago I went to her place to tell her I have cancer, and her response was this "Well, your dad will be happy to see you". WTH? I'm NOT dying and in fact, caught this so early, I fully expect a compete cure.

Even if I was actively dying--what a thoughtless thing to say to someone.

I keep trying to have a good relationship with mother and I now have simply given up It's too stressful and depressing. She becoming forgetful and says whatever comes to her mind and it's not usually nice.

I talked this over with my YB who is pretty much as off board as he can possibly be. Told him what she'd said, etc and told him I was going 'grey rock' on her ( there's a post dedicated to that going on!) Said he ABSOLUTELY HAD TO STEP UP whether he wanted to or not. I cannot and will not do any more steppin and fetchin for her.

His response was that he felt really guilty and bad, he was always happy to let me handle the 'garbage'---but not any more. For the first and only time in my life I am putting myself first.

Whether TB contacts my 2 sisters and the brother with whom mother lives--I don't know. And I don't care.

Sometimes self preserving is being tougher than you think you can be. This is not what I want, but it's what's best.

Might be best for you to walk away, too.

RUN don’t walk away from this situation. Your father was verbally abusive when you went out of your way to help him. Your sister is being psychologically abusive when you’ve gone out of your way to help her. Enough is enough. Cut your ties and move on with your life.