The Firstbyte time
Ideally should be around .30 – .50 sec. Check on unused plugins and remove them and check which plugins are executing slowly on both sites using the F-12 Profiler plugin.
Check the sizes on your combined CSS file, maybe removing unnecessary plugins will get that size down.
Remove social media share plugins mostly they have trackers in them rather then APIs to share content, for example, the Facebook tracking javascript in some plugins is 1/2 MB and should be removed
Remove various other javascript files that may be unnecessary that might be able to be removed to save significant size.
Total website size ideally like to see under 1mb or 1.5 MB and at worse 2mb in size if absolutely necessary.
Load times Ideally would prefer to see 1-2 secs max or even less if possible.
Watch for an enormous amount of network payload, youtube, facebook etc possibly taking over 2.6 secs to execute those unnecessary javascript which are mostly tracking people.
Maybe your first byte slow time is not plugins but the actual server often times shared hosting is just to slow and will have some times being fast and others to slow so check at different times to find out.
you need to compress objects (js,css, html, images etc) and some objects may not be browser caching while some are. We want browser caching on all of them if possible.
Social share scripts have to go or a find a better alternative that doesn’t rely on all the javascript, even though usually these objects are browser cached in the user’s browser they are still being executed. The youtube javascript video player file alone uncompressed is 1.4 MBS in size ideally we are looking at the entire page to be 1.4 MB or under then all the social trackers are executing in the user’s browser, ideally, get rid of the social especially on the home page where the majority of the traffic comes in because it is adding way too much weight and use html5 to play videos natively from the server and not youtube js player that is over 1b in size when this capability is already built into the browser.
There is a lot of work to do on the sites and not just the home page but all pages will likely need image optimization on the entire media library.