Is there any question of self-dealing in your proposed course of action? Surely the PR cannot buy out a share of the estate whether he wants to or not, and whether the other sibling consents or not.
It all sounds rather complex and, bearing in mind the PR just wants to do up the house and “flip” it, I find myself wondering why he doesn’t just sell the deceased’s home and use his inheritance to purchase a different property…
You can always overcome self-dealing restrictions if you have the consent of the (all adult) residuary beneficiaries. You can do what you like with full consent.
Quite apart form any question of self-dealing, there is the issue summed up above in the phrase, “The other sibling will need to ensure that as part of the buy out he is released from the mortgage.” This is easier said than done. The mortgagee is under no duty to release anyone who is subject to the obligations of the mortgage. It will most likely have lent on the basis primarily of the borrower’s covenant to pay and secondarily on the security - See Nykredit v Ed Erdman Gp (No 2) [1997] 1 WLR 1627 HL. On the assumption that immediate redemption in full is not intended, it no longer has the benefit of the borrower’s covenant and is unlikely to release anyone who might be liable, at least unless and until it is satisfied that any new proprietor can satisfy its lending criteria. It is likely instead to demand immediate repayment and if not repaid take steps to exercise its common law right to possession and its statutory power of sale under LPA 1925 s 101.