A transfer of a going concern for VAT purposes is when a business is sold by one organisation to another. Reading your question, I don’t think that is what’s happening here.
Given your mention of the VAT2 form, I’m assuming that you and your brother currently have a partnership VAT registration, and you’ll be removing him and adding your wife. In which case, according to HMRC’s manual https://www.gov.uk/hmrc-internal-manuals/vat-registration-manual/vatreg35200 there won’t be any change to the VAT register – the same VAT registration will be receiving income from tenants before and after the change.
Who has opted to tax the property – you and your brother individually, or the VAT registered partnership? I suspect that it’s the latter – if so a sale of your brother’s share to you can’t really be a supply by the partnership, so wouldn’t be impacted by the option to tax.