Vuetify component v-form is not responding on the declared @submit event handler
Your submit button isn't inside the form so it's not triggering a submit event.
Either re-structure your markup or try setting an id on the form and use the form attribute on the button, eg
<v-form @submit.prevent="checkLogin" id="check-login-form">and
<v-btn type="submit" color="success" form="check-login-form">Login</v-btn>Note: The form attribute does not work for any version of Internet Explorer.