If the mother has no will, can the biological, adult daughter become administrator even if mom is remarried but estranged?

In the absence of a will the spouse would have the first claim to be administrator and the deceased children would have second place. Meaning that if there is no legitimate objection to the spouse, the spouse would get it but if the spouse had a criminal record, does drugs, stole estate assets, etc. then spouse would be removed. Be careful here, removing or challenging the spouse doesn't mean you will be appointed, often when relatives battle the court will appoint a lawyer as executor, and the bills are often exactly equal to the amount of the estate.