The Yorkists probably would accept Jasper, seeing how it's a Yorkist who's reigning in this scenario.
You're right about the jealousy stuff tho.
I don't see the Edwardians siding with Lincoln/Warwick, but an alt Richard of York is a possibility
Why not Warwick? He was a legitimate nephew to Edward IV, so he's preferable to Jasper. And also, Lancastrians would see Jasper's marriage to EoY as a betrayal and probably would move on to supporting Edward Stafford (or, if Lancastrians don't want a child, that some of them could issue a fake of Henry VII's will in which he legitimsed Charles Somerset as a son of Henry Beaufort and named him his heir, I think John de Vere would prefer Charles I Beaufort to Jasper Tudor).