Single Wordpress site in two languages

how to create a wordpress site with two languages with a switch button

Try qTranslate.

Or Google Translate + WPML

It’s very much easy stuff, don’t go for two website. Instead of creating two websites create translator of page in WordPress and that will help you while in marketing. Because if you will create 2 same website with same content then Search Engine will consider as duplicate.

I also recommend WPML. It is what I always use.