Best order of travel

I don't think there is any magic to one schedule or another. Put some pins in a map. We generally try to travel in a straight line so we are not back tracking or overlapping. Flying, maybe using a discount airline, would be easiest from Germany to Scotland just become of the distance and the water.

Thanks Frank! Good advice

Perhaps plan it as three movable components and then start playing with your flights and see what you can make work.

Regardless of the order, between any two of these three destinations, I'd fly. Look on Skyscanner for flights: https://www.skyscanner.com/

To see who flies nonstop from an airport, look at that airport's Wikipedia page. And be creative. For Scotland, Edinburgh and Glasgow airports will have the most options, but I see that you can fly from Zurich to Inverness, if you want to be closer to northern Scotland: https://en.wikipedia.org/wiki/Inverness_Airport#Airlines_and_destinations

I would go first to Switzerland, then Germany, ending in Scotland, or the reverse.
Air would be my choice between Germany and Scotland.

It would help to know which part of Switzerland you'll be going to for your mothers heritage. And what else you would like to see in Switzerland. Consider taking a boat between Hamburg and Scotland, you may find it very pleasant.

no boats between Hamburg and Scotland unless you want to sail your own

Do remember you can typically save $100-$125 per plane ticket if you go into Scotland and home from elsewhere in Europe because you can avoid the U.K. Long haul departure tax. (The short haul departure tax is pretty marginal)

I would start by nailing down at the very least a list of the places you most want to visit and roughly how much time in each. Once you have a "skeleton" it's easier to determine a route, note if there are any places either nearby or on the way from point to point that are of interest to you. In my experience, it's a lot easier to fit flights to an itinerary than to fit an itinerary into flights. If you are going in July-August, weather won't be a determining factor. Local festivals might be. The one that comes to mind immediately is the Edinburgh festival. Then decide if you want to be part of it or to avoid it.

Without doing research, my first thought is fly between Scotland and/or Germany/Switzerland. Between Germany and Switzerland, it depends on where you want to go in each. Germany's a big country. For instance, if you only want to spend time in Hamburg/Schuby and, say, Berlin, then you'd fly to Switzerland. If you are planning to travel south through Germany by train (or even by car) visiting several points along the way, then you might want the train to Switzerland or even continue with the car.

Bottom line - until you decide which places you want to see in each country, there are too many unknowns.

no boats between Hamburg and Scotland unless you want to sail your own

Now granted, I wrote that without checking online, as I don't have good Wi-Fi here, however I was quite sure that there is at least a boat between Newcastle and Germany or Hull and Germany, and whilst they are not exactly Scotland there are a lot closer than the south coast.

Hull to Rotterdam or Zeebrugge

Newcastle to Amsterdam

that's all!