...Britain and Ireland are basically in personal union with the Wittelsbach Palatine.
England, Scotland, and Ireland, except the union won't exist until
both Elizabeth and Frederick are succeeded by their eldest son. And Elizabeth lived until 1662 OTL.
An important point is which of them passes first; the heir will inherit that realm, while the surviving parent continues to reign in (or claim) the other. OTL, Elizabeth outlived Frederick by 30 years.
In any case, the Palatinate is only a claim for them; in OTL, Karl Ludwig (the second and eldest surviving son) didn't get it back until 1649. Frederick may have a better shot at reclaiming it with serious English backing.
And a butterfly knock-on: the 1629 accidental death of the eldest son, Henry Frederick, doesn't happen.
So there are all sorts of ways this could go. If as OTL, Frederick dies in 1632 and Elizabeth in 1662, their heir (assume Henry Frederick) will be actual Prince of Wales from 1629, and nominal Count Palatine from 1632 until the Palatinate is regained (if it ever is).
Or try this: Frederick, with English support, regains the Palatinate in 1635, but dies in 1638. Henry Frederick succeeds as Count Palatine, and reigns there. This creates an awkward situation for England, with the heir to the throne out of the country. Perhaps Henry Frederick names one of his brothers viceroy instead. That seems reasonable. (Though Henry Frederick may prefer ruling his own domain to hanging around as a powerless heir. And it's entirely up to him.) Elizabeth passes in say 1656, and Henry Frederick succeeds in England.