Is there a nice way to pass props to the parent component with Vue router?

Use route meta data:

path: '/form',
name: 'Form',
component: Form,
children: [
  {
    path: 'step1',
    component: FormStep1,
    meta: {
      title: "myTitle In Header In Form Component"
    },
  },
  {
    path: 'step2',
    component: FormStep2,
    meta: {
      title: "myTitle is different In Header In Form Component"
    },
  }
]

And then in your parent component:

computed: {
  title () { this.$route.meta.title }
}

If you prefer title be passed as a prop to you parent component, use:

routes: [{
  path: '/form',
  name: 'Form',
  component: Form,
  props (route) => {
    return {
      title: route.meta.title
    }
  }
  children: [ ...

You could also make title inheritable. For that you need to use a bit more complicated check:

const matched = route.matched.slice().reverse().find(route => route.meta.title)
matched.meta.title

Note: that slice() seems to do nothing, but it is creating a copy of matched array so we don't modify the original array - removing slice() will ruin your day with debugging.

You are nearly there, just emit from child to the parent with the value of the prop received.

      path: '/form',
      name: 'Form',
      component: Form,
      children: [
        {
          path: 'step1',
          component: FormStep1,
          props: {
            title: "myTitle In Header In Form Component"
          },
        },
        {
          path: 'step2',
          component: FormStep2,
          props: {
            title: "myTitle is different In Header In Form Component"
          },
        }
      ]


//Inside FormStep2 and FormStep1
created() {
    this.$emit('childinit', this.title);
  },


//inside Form
methods: {
    onChildInit( value ){
      this.title = value;
    }
  }

To make things cleaner, consider creating another layer of children inside your router, so you don't have to emit on every child. Here's some code out of a project I'm looking at right now that does something very similar notice the step prop which I'm passing about.

//inside my timelineBase component I listen for onChildInit, set a method to grab value from the child, then use that in the layout to tell pageStepper what section I'm in.

<router-view v-on:childinit="onChildInit" :key="componentKey"></router-view>
<pageStepper :step="pageStepper"></pageStepper>

//code has these props. props: ['mode','step','componentKey'],

This is my routes.

const router = new VueRouter({
    routes: [
      {
        path: '/',
        component: Layout,
        children: [
          {
            path: '',
            component: homepage,
            props: { cssClass: '' },
          },
          {
              name: 'addTimeline',
              path: 'timeline',
              props: { mode:'add', step: 1, componentKey: 0 },
              component: timelineBase,
              children:
              [
                  {
                    path: 'add',
                    component: timeline,
                    props: { mode:'add', step: 1, componentKey: 1},
                  },
                  {
                      name: 'updateTimeline',
                      path: ':id/update',
                      component: timeline,
                      props: { mode:'update', step: 1, componentKey: 2 }
                  },
                  {
                      name: 'addEvent',
                      path: ':id/event/add',
                      component: addevent,
                      props: { mode:'add', step: 2, componentKey: 3 }
                  },
                  {
                      name: 'editEvent',
                      path: ':id/event/edit/:event_id',
                      component: editevent,
                      props: { mode:'update', step: 2, componentKey: 4 }
                  },
                  {
                      name: 'previewTimeline',
                      path: ':id/preview',
                      component: preview,
                      props: { step: 3, componentKey: 5 }
                  },
              ]
          },


        ]
      }
    ]
});