first trip to Ireland and Scotland and need help with itinerary!
First question is ... how long are you in Ireland before heading to Scotland? You have Day #5 with ? but is that the end of the trip and on to Dublin?
The logical route would be up to Dublin to get over to Scotland since you're in Cork ... and the bigger question is what do YOU want to see and do? Waterford? Kilkenny? You say more outdoor things so Wicklow National Park before going to Dublin head to Scotland.
You do have to return the car in Ireland and get a new one in Scotland I'm afraid... and I wouldn't take a day trip to London. It's 4 hours by train, minimum ... so you're spending 8 hours in transport? If you had more time in Scotland then you could drive down ... and fly home but my experience has been that splitting Ireland/Scotland, folks just don't give either the time they deserve.