What recourse do we have if the caregiver sibling refuses to communicate with all other siblings regarding deceased parent's estate?

So you do not even know if there is a will or not at this point?
It is likely time for the four of you to spend about 100.00 each for an hour of a lawyers time. You will find out how to follow up on probate, finding out who is on the deed to the home (if there was one) and etc. in your area. You will then know how best to proceed about having an executor appointed to do a probate, if there is not will or trust.

It is truly sad that siblings find themselves in this situation. I know of so many stories where parents trusted children to be fair with one another. Guess what? Sadly, this doesn’t happen and there is a big mess.

Contact an attorney to get answers for your state. Best of luck to you.

So Mom has died and Dad is alive? Unless you have access to your Father's and your Mother's wills there is no way you can know anything short of asking. I am assuming your sister, caring for both parents, is the POA. Since she is giving all care for two parents, for all this time she is more than likely in charge, and also likely to be the executor on any will. You are likely safe in assuming that the Mom's death left any deed to property/assets in her husband's name, with Sister as POA. But short of assuming, that's about all you have. Almost certainly she will be executor. If there are any assets left then your Sister may be sole beneficiary in thanks for all the care she has given. But be that as it may, if there is a will it will have to be recorded when filed for probate and that's a public document. If money is in a trust, nothing needs to be filed, so it is basically a wait and see thing. No one has any right to question. Should you suspect fraud or abuse you can open a case with APS, but I would have your evidence of same at the ready.
I honestly think that the Sister who is doing direct care SHOULD have the authority, but that's me. Were I to want relationship or access I would offer what help I could with cooking, cleaning, respite care, and etc.

Unless there's a piece of paper saying she's the sole authority, she isn't. Does anyone know if there's a will or trust in place? You need to find them if there are, because they'll be the ones that say who is the Trustee or executor.

If there is no will or trust, then your parents died "intestate" (not interstate), or without a will. The courts will decide who is their representative, not you and not Sis. No one can sell or distribute anything until probate court decides who has the authority to do so. It is illegal to do otherwise. (You might remind your sister of that fact.)

You and your siblings need to consult a trust and estate attorney to find out what the next step is, because right now everything is legally in limbo.