Not sure how having another woman in the household would affect Edward's familial policies so drastically.
Elizabeth would most probably see Richard as a 'kid brother' and would probably not oppose his match IMO.
Better if you have Mary and George, more realistic.
You have read the thread BEFORE contesting my choices on the base of the OTL personalities of people who here are very different?
Elizabeth of Lancaster/Bedford is a very influential Queen Consort who pretty much hated the Nevilles (and NEVER trusted her mother-in-law or brothers-in-law and AFTER George’s betrayal she would NEVER be favorable to another Neville in the family).
Plus the ATL rebellion of Warwick and George was born exactly from Warwick’s tentative to impose to Edward and Elizabeth a French match for the Prinse of Wales and to marry his own daughters to Edward‘s brothers (and the King and Queen were already pretty much set against both things). Plus George here can get only the lands of the Countess of Warwick as all the lands held directly by Warwick and Montagu were lost with their attainders (and eventually he will be still executed and attainted for treason).
And Elizabeth’s influence, having sons early and his wedding being a strength instead of being a problem, and his rule being much more secure than OTL, made Edward a much more determinate King and less easy to influence than OTL