Can I bill an estate after my dad passes?

Unless you have a caregiver contract, you cannot bill the estate. If your father is staying in your home and there is no money, does he qualify for Medicaid? You are in a very ugly spot and unless your sister relents or your father changes his power of attorney to you, you have little recourse after he dies. If he goes into a facility for long term care, the house will have a lien put on it anyway; and there may be no selling any house for anyone's benefit.

Without a caregiver's agreement between your dad and you that you both sign, you are not going to bill his estate which you say is limited.

Why isn't your rich sister taking care of him?

Is he competent to sign an agreement between the two of you? I would suggest getting a lawyer if you go this route.

Birdypie, regarding the house, since your Dad left the house to both of you while he is alive, and the Deed is now in both of your name's, then there will be Capital Gains Taxes that both you and your sister would need to deal with if the house is sold. And since neither of you are in residence, the house may be deemed an "investment property", thus no capital gain deductions.

The bases for the taxes will be the price that your Dad paid for the house. And sometimes there would be a Gift Tax that Dad would need to pay depending on the value of the house.

If only your Dad would have left the house in his Will, instead. Less complicated tax wise.

Now, when the time comes and Dad passes, chances are his estate will go into Probate. You could try saving all the receipts that you paid for out of your own pocket, and present those to the Probate Judge. The Judge may or may not take those receipts into consideration. It's worth a try. Put everything into a 3-ring binder. Copy of the bill along with the copy of the check. I use to put the check onto top of the receipt so I would only have one page to deal with.

Can your sister buy out your share of the house? That would solve a lot of financial issues that you have. If sister says "yes", then the both of you need to agree on a licensed Appraiser to give you both the market value on the house.

Billing estate after death could possibly work IF there was a promissory note or memo of understanding done while dad alive AND you file it to be a debt of the estate AND THEN whomever named executor accepts the debt (unsecured) as valid with $$ in the Estate to pay debts in whatever order required by probate laws. 

If he’s moved to another state to live with you, so he’s a legal resident of your state, then usually probate is opened in state of his death. Would he actually have any Estate? It reads that the house was already moved into both you & Sissys name, so that’s not an asset anymore. Any $ anywhere else? If not, there’s nothing to probate. 

But later in your posts, you mention his using “his $ to maintain his house”.

So exactly what is the legal ownership on the house??? 
And who exactly is paying all of the many many property expenses???

If house already moved out of dads name, then what I’d more concerned about is your share of ownership on the house. If Sissy is paying all or some of the property costs, & if she wanted to be very pit bullie with you, she could place a lien on your share of the property for all costs paid by her for your share. If it was moved out of dads name properly then it has no more of his elderly homestead exemptions. Taxes on it could be significant, plus insurance, upkeep, etc. If this is a lower value house, a few years of her paying your share could wipe out your share of ownership. This is often done to remove a non performing owner from jointly owned real estate. You might want to think about having house forced to go to sale or have Sissy buy out your share, and do this ASAP. You need a real estate atty to do this & needs to be atty in the state where house is. The good part is that atty can be paid from house sale proceeds. 

You can claim back money you've laid out on goods or services for your father from his estate - in effect, you've lent Dad the cash and you are his creditor. Submit receipts with an account and you should be fine.

If you have POA for your father's medical and welfare decisions, then your decision that he was not thriving at home and required a higher level care was legitimately taken and you should not be paying for his in-home care. You can't claim compensation for your own time or work, but you certainly can claim for agency or professional fees.

What was your sister's objection to removing your father from his home?