We have a similar story in my family. My dad's done all the work on his side and I've done a bit on my mum's side.If some guy hadn’t decided to uproot himself from Italy five hundred years ago and move to Scotland
My dad mother's side is from a French Huguenot family who left France in the events in the aftermath of the French Wars of Religion which had won the Huguenots religious freedom, but was eroded away again till the treaty was revoked in 1685.
My surname most probably comes from Old Norse and thus could have over anywhere from the 800s when Vikings started to settle to 1066 when the Normans (North men ie from Scandinavia) came over.
And my mum's mum is Dutch and met my grandad in the aftermath of WWII. He had been too young to see much action, but was over there on peace keeping duty. I haven't done any research into this side yet.
My English grandfather's side is the most dull, mostly farm labourers and such.