If you want to open a website into anything other than your current or a new browser window, you will need to provide a container for it. You can use a web object for that.
Have your button just open a new slide or layer, as usual. On that slide or layer, insert a web object. Use your URL as the address in the web object. Set to display in Slide and load automatically.
Using a layer is also the easiest way to display it in your current slide. Otherwise, since you can't normally make the web object hidden, you would have to push it back on the timeline and maybe jump to a cue point to display it.