The Dvorak keyboard layout on Macintosh already has international character support, the exact same support found in the US keyboard layout. There is no need to switch from one to the other if your primary language is English and you need to type occasional words or sentences in other Western European languages.
I have been using the Dvorak layout on Mac since about 1988, and for all the years since then, I have been using it to type in English, French, Spanish, Italian and German, without any modification or re-mapping of keys at all. The "dead-key" diacriticals are all available; it is only a matter of memorizing their locations.
Dvorak with Option key held down to show "dead-key" diacritical combinations along with other characters needed in Western European languages
U.S. layout with Option key held down to show "dead-key" diacritical combinations. Note that the exact same set of "dead-key" diacriticals are available on both the Dvorak and U.S. layouts, and they are assigned to the exact same keys although those keys are of course in different physically-mapped locations. The same goes for all the other characters used in other Western European languages.
If you need other characters that are not provided on either the U.S. or Dvorak keyboard layouts, then of course you should investigate other keyboard layouts specific to other countries, nationalities and languages.
[Just last week I had to use Adobe InDesign and WordPress to handle text from an orchestra concert program including two words in Czech with characters that I had not encountered before, and neither of these keyboard layouts provide support for that!]