It's the incorporation of Wales into this that's a problem, because Scotland taking Ireland is quite doable if you pick the right spot. Otherwise, the Welsh were constantly at odds with England or sat and bided their time neutral to all. There's little incentive for them to unite with Scotland if they can remain independent themselves, and unlike common perceptions for a reason I've never understood (not suggesting the OP is guilty of this) two countries agreeing to merge was not a regular, or even in many cases plausible idea. Really you need Wales to become a vassal of Scotland, and there's only one time I can think that this was ever a possibility - I believe that the Welsh offered their allegiance to the Scots in the most unstable years of Henry IV's reign, though it was almost a token gesture and the Scots would never have been able to capitalise. You'd need to make the Scots much stronger (you can start by having them keep Northumbria circa 1080) and make the English much weaker, somehow, but still strong enough to partially subdue Wales. Then you'd need to manufacture an event where England suffers a temporary bout of extreme weakness at which point the Welsh feel their odds are better trying to "defect" to Scotland rather than going it alone.
The concept of pan-Gaelic nationalism and unionism is a very modern concept, and while Scotland and Wales associated with each other, they associated with each other for the reason of their mutual antagonism with England. There really won't be any drive for a united Gaelic state, and unless you decide to make a personal union of the thrones (remember that Wales was multiple states for quite a while, so you'd need to bide your time patiently) then the only other option as mentioned is vassalage.
Ironically, while England will probably continue to be "the old enemy", Perfidious Albion, Scotland in this scenario will likely come to be seen as an unwelcome dominator in the union, and I don't see them handling Ireland any better than England did. In fact, due to the very frail Scottish economy, you could make a very strong argument for the idea that Scottish rule of Ireland would be far less capable of responding to problems such as rebellions and potato famines, so you could even see Scotland becoming portrayed as the evil Gaelic empire by its own subjects outside of Scotland. Would make an interesting change from England being the Devil Incarnate...