siblings differing valuations, help needed

Marlon, I have been trawling through probate/executor/will threads on quite a few forums, largely UK based, and I have seen one or more threads by people in the later stages of your current position.
In at least one of those threads executor A (call them Tom) bought executor B's (call them Harry) share of the asset/house in question for an agreed and pro rata amount at the time of sale. Sometime later Tom sold the asset/house for a 'profit', Harry then came after Tom for a pro rata portion of the profits. If you do buy your brother out I suggest you take advice and steps to protect yourself against such action.

On DeiseBlue point about requiring his signature to sell the house... I think if you apply to the High Court, with your documentation, having made all reasonable efforts.. then the Court can direct a court clerk to sign on the problem executors behalf...

It's a tricky situation... just keep all notes, involve your solicitor as appropriate, make your offer of either, him buying you out, you buying him out, or selling and splitting... if nothing works eventually you'll have to go to Court.. in Court they should find that you have been reasonable, and he hasn't.. and as I say, the Court has considerable powers.. while it may take a while, and cost money, the court won't allow a problem executor to hold up things for ever...