родительский компонент:
<component-one v-on:click-some-button="hideBlockkInOtherComponent"></component-one>
   <component-two ref="othercomponent"></component-two>
methods: {
    hideBlockkInOtherComponent () {
         this.$refs.othercomponent.hideBlock();
    }
}
component-one:
<div><button v-on:click="sendClickForParent">click</button></div>
methods: {
    sendClickForParent () {
         this.$emit('click-some-button');
    }
}
component-two:
<div>
       <div v-if="showBlock">my block</div>
   </div>
data () {
    return {
        showBlock: true,
    };
},
methods: {
    hideBlock () {
         this.showBlock = false;
    }
}