Hi Andrew - I'm sorry to read of your loss and for the frustration felt re how to update the register.
If they were joint owners then we can't update the register to say No owners due to both deaths
Our online assisted guidance is designed to walk you through a series of Qs and the answers then link you to the guidance you need both for transferring it now into your names or one of you buying the other out and again transferring the ownership
HMLR Guide: Start - External · HM Land Registry
A couple of things to note/consider would be firstly we don't need both probates, just Mum's as the property forms part of her estate and it's for her executor(s) to then deal with. We will still need a copy of Dad's death certificate or probate to confirm his demise though.
Secondly you don't necessarily have to update the register now and then buy your brother out. The deaths are very sadly factual and the property remains part of Mum's estate until the executor(s) deal with it. Updating the register can as a result wait but I do appreciate why you might prefer to update it now. If you do and the executor(s) transfer (forms AP1, AS1 and ID1/ID3) then a second transfer from the new legal owner*s( to just you can then be made at a later date (forms AP1, TR1, ID1/ID3) as appropriate -
Registering land or property with HM Land Registry: Change the registered owner name - GOV.UK
I hope that helps and doesn't add to any confusion - have a read through the linked guidance and forms and if more Qs arise then do post again
We can't advise you on what's best to do or explain how wills/inheritance works for example but we can help re the forms needed once you've decided what you are going to apply for.