How much of a difference would make if Battle of Tewkesbury would have end with a complete victory of House of Lancaster instead? Any long lasting effects on English monarchy and future succesion system?
TBH, I didn't though about that. Good Point, but perhaps there is still a chance for a victory against the odds - maybe all Queen needs is for Edward York to get an arrow to the eye or have a tragic horse accident during charge?The preferred outcome for the Lancastrians in that campaign would have involved them not fighting at Tewkesbury at all. Queen Margaret was a good strategist and she realized early that she did not command a sufficient force at the moment to fight Edward and his army.
In OTL, Margaret was up against heavy odds at Tewkesbury. Edward successfully managed to maneuver Margaret into a bad position. In fairness, her plan deserved to succeed. It was a great plan and almost worked. It's to Edward's credit that he reacted to it so well.
If Margaret wins any kind of battle at Tewkesbury, it's one that sees Edward decide to withdraw after suffering heavy casualties. Margaret immediately finds a way to get the remainder of her army into Wales, but now it will take even more time and money to raise the needed troops to raise her army into something that can challenge Edward.
Had Margaret been allowed passage through Gloucester, she would have successfully escaped into Wales, regrouped with Tudor, and consolidate her positions. The entire war would have dragged on longer, buying more time for Margaret to tussle up more support, allowing more time for her own son Edward of Westminster to gain experience and learn on the job, and most importantly, sire his own children, sons particularly. A Prince Edward now of age is the undisputed leader of the Lancastrian faction and is officially claiming for himself his birthright to the crown of England. Margaret's immediate task to guide her son to this point would have been more or less successful, given the circumstances. She somehow managed to guide him along this far, sacrificing everything for his cause. She would still continued supporting him, but she would no longer be burdened with overall leadership of his faction.