Pretty sure Vuejs makes it very hard to directly use external html.
v-html will simply replace the html content and therefore will not execute any directive. The purpose of it is to avoid XSS attacks as documented here: https://vuejs.org/v2/guide/syntax.html#Raw-HTML
Dynamically rendering arbitrary HTML on your website can be very dangerous because it can easily lead to XSS vulnerabilities. Only use HTML interpolation on trusted content and never on user-provided content.
If you really need to use external html, it is possible to use
Vue.compile() documented here: https://vuejs.org/v2/api/#Vue-compile
A working example can be found here: https://jsfiddle.net/Linusborg/1zdzu7k1/
and its related discussion can be found here: https://forum.vuejs.org/t/vue-compile-what-is-staticrenderfns-render-vs-staticrenderfns/3950/7