Hi Rail. I'm glad you found this article useful. You can use a single recaptcha instance as many times as you want. All you need to do is to call the this.$recaptcha.reset() method after every use.
That way, the token used for the previous verification is reset.
Also, you can setup the recaptcha instance in the child component and everywhere that component is being used, you will have a new instance of it running.
Just make sure you don't forget to call the this.$recaptcha.reset() after every use. Whether it was successful or not. It's pretty important.
If this isn't clear enough, please let me know.