What's the weather like in Edinburgh/Aberdeen area usually like the end of May. Will we need a raincoat and also a jacket for warmth?
I was there in May and it was beautiful, no rain and comfortable (mid 60's).
Be prepared for anything from cool or cold and rainy to comfortable and sunny. You can probably rule out only freezing cold and really hot.
Take a light packable wind/rain coat (with a hood is a plus) with little or no insulation and bring a wool sweater and wool cap or hat to stay warm. When it rains, it's likely to be windy so a travel umbrella will rarely be a good alternative if you spend any time outside.
Never go anywhere in the UK without rain gear. You can't let a misty day stop you. Do layers. Get a good gortext jacket and where sweaters under it for warmth. My parents were in Orkney in June and were very glad to have their lined jeans from LL Bean.