You could use v-if or v-show for conditional hide show the Book RentDate on changes of boot type.
The directive v-if is used to conditionally render a block. The block will only be rendered if the directive’s expression returns a truthy value.
<h1 v-if="awesome">Vue is awesome!</h1>
Another option for conditionally displaying an element is the v-show directive. The usage is largely the same:
<h1 v-show="ok">Hello!</h1>
And for this error $refs.qDateProxy.hide, you can create a method and inside of this method you can use like below
onRentDateChange(){
this.$refs.qDateProxy[0].hide()
},
You can check here with working codepen.io.
EDIT
As per OP's comment, I have updated codepen.io. I have taken boolean variable inside of this.$data.Books array and used .find() method of array for changing variable status.
onValueChange(val,id){
let rec = this.$data.Books.find(({ID})=> ID==id);
if(rec) rec.isRentShow = val == 'Rent';
},