This should get you on track…
<iframe src="https://wordpress.stackexchange.com/questions/224947/javascript:void(0);" frameborder="0" style="display:none;width:100%;margin:0;padding:0;" id="fullsizeframe"></iframe>
<a href="http://website2.com" onclick="loadfullsize(this.href);">Website 2</a>
<script>function loadfullsize(url) {
fullsizeframe = document.getElementById('fullsizeframe');
fullsizeframe.href = url; fullsizeframe.style.height = window.clientHeight;
return false;
} </script>
Note the problem here is you have to insert the iframe HTML directly after the <body> tag (and have no CSS width rules on the body tag) for this to work or the iframe width may be limited to less that full width if inside other containing divs etc.