For the England part of your trip. For the he Tudor aspect you must visit :-

First and foremost Hampton Court Palace... and if you get time time, The Tower of London. (The Tower has very long tourist queues in July.) Your wife should know all about them and it will bring to life their history by being there.

Outside of London, although Jacobean... Hatfield House in Hertfordshire 30minutes by train from London. which has portraits of Queen Elizabeth of England. Elizabeth was here when she was declared Queen and held her first council of State in the Old Palace.

I will leave the Scottish part to those with more knowledge north of the border.