I know this isn't what you asked, but if he has an older son there likely wouldn't have been a Bosworth. Richard lost a lot of support when his heir died; one of the reasons his rule was acclaimed was that he represented stability and avoided the plague of a minority rule/further succession crisis. When his son died, suddenly a future succession crisis seemed all too real and even if he remarried and produced more heirs, they might very well be children at Richard's death. Others, too, saw his childlessness as god's judgment for his nephews, which seemed proof of his guilt in a very superstitious age. Richard himself seems to have become more bitter and less concerned with his popularity after losing his son (and wife).
An older male heir precludes all of that, so many who turned or wavered might very well not have.
That said, if his son is around 15 for a Bosworth, he's there. Richard, like his brother before him, put a lot of stock in martial valour...both had lead men into battle in their mid-teens, as had their brothers. Even the famously protective Margaret had allowed Prince Edward to take the field in his teens, much to her regret, because it was expected of royal teens.
Now that being true, the battle might have gone differently even if the dispositions had been the same as in real life. For one thing, though Northumberland would likely still retained much practical authority, it's probable that the Prince of Wales would at least have official/moral command of that battle (or much less likely the van) and in that case it seems impossible that Richard's left would just sit out the contest. Therefore it seems much more likely the Stanleys choose a different prevailing wind, and very unlikely Richard needs to lead that doomed last charge.
Those aside, if we assume all happens as in real life and the Prince survives, it's a very different scenario. People forget that even with the obvious heirs to the York line dead or doubtful, Bosworth was not the final act; Stoke Heath was one of the larger battles of the Cousins War, and that's with a dormant period and probable pretender. If the legit Prince of Wales is still out there, many forces will flock to him, particularly from the North and Ireland. Henry Tudor's support was buoyed by the very sense that he was an end to it all, however dubious; that's not true if Richard's son lives and leads an army. Additionally Burgundy probably lends a significant hand; his aunt would support him without a doubt, and there's the Burgundian need to balance French investment.
As mentioned, I think it improbable that a Bosworth does happen or follows the real life model in this scenario, but if it does I think the Wars of the Roses might well go on for much longer.