Can you open probate without both trustees
in agreement?
Just a bit of language clarification. The person appointed by the court to be responsible for administering a probate estate is variously referred to as an executor/administrator/personal representative, depending upon what state you are in and whether there is a will or not. A trustee administers a trust.
A will only nominates the personal represetative(s). The court appoints. You may have to jump through some hoops and hold your sibling's toes to the fire to either assume the co-personal rep position or waive his/her right. But, no court is going to refuse to open probate just because one of the personal reps nominated in the will wants to diddle around. If need be, consult with an estate attorney to find out what those hoops are in Arkansas.
(What do you mean by "paranoid?" As in, has a diagnosed mental illness?)
Addition:
If it were me, I would shoot for knocking the sibling out of the estate administration completely and be the solo administrator. Co-administration can be a real pain in the best of situations. Judging by your sibling's attitude so far. you & sib might have the long knives out before it is all over.