I tried to do it with iframes but when I click a link in the child wesite then it leaves the parent website
how can I keep the parent website but still interact with the child website?

most likely cause is that the links in your iframe have a target="_top" attribute

If the child site is not yours, it has a framebreaker,
something like

   <script defer='defer' type='text/javascript'>
    if (window != top) { 
     if (top.location.href.indexOf("translate") < 0) {

Doesnt break valid reason for a frame, google translate

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