Bert, the öäü are on my keybord that's how I do it and I never gave any thought til now what the computer does after I hit the key.
I have a comparable problem with ñÅÆ. I have to cut&paste them from the extra character section (or however that's called in English) of MS-Word.
And to find $ now took me about 3 minutes whereas you'll find that on your keybord I guess.

Wolfgang