My sister assured me that my late fathers estate would be shared equally (he left no will). She is not honouring this despite it being my fathers wishes (verbal). Is her verbal agreement / promise binding?

Not really, after his death in most states wills have to be in writing and signed to be valid. In some cases video or recorded wills are allowed.

BUT, if there is no will, then all specific heirs have equal rights, and your sisterr has no right actually being in charge of it, unles the court probate has appointed her.

Sounds like time to get an attorney before all the money is gone.