What to do when sibling tries to prevent me from acting as my mother's POA?

Consider changing the mailing address on everything to have it forwarded to your address; you can do this by taking your POA documents to USPS.
Be certain to keep meticulous records. You are responsible for accounting for every single penny in and out of all of Mom's accounts. That means a file folder with a file for every single entity you deal with with your Mom's things. Be certain all are notified you are her POA and handling all finances. If Mom is competent consider giving her a small spending account of her own which you will monitor to be certain that it is well handled. Cancel all charge cards.
This is a difficult job. I did it as POA and Trustee of Trust for my brother in his last years. I know! Do not share information with siblings. It is not their information. You were made POA by your Mom.
If your siblings are very meddlesome you may be called to court at any time in a guardianship action or any other action. Keep a diary of their interference and of all else involving your Mom. A composition book with no tear out pages, and with ink and cross outs only. This is GOLD in a court action.
Best to you. I understand how difficult this is. After a year or so the ducks will be lined up and marching along better for you.

Medsister, confused by the sentence "acting as a my mother's power of attorney". Do you have a signed legal document where your Mom appointed you as her POA? If not, then you cannot "act" as her POA. Please clarify, as that will help with us answering your question.

Do you have a legal POA that in effect. You can't simply "act" as POA. Your mother has to legally give you POA.