And do you want the re-designing on the same platform? (Squarespace)
I would recommend creating a website on a Wordpress platform because:
a) It comes with extremely simple admin panel that any non-technical person can understand and implement changes in the website through it
b) It allows maximum on-site SEO configuration w.r.t primary keywords on H1, H2, H3 titles, tags, meta tags, slugs, URLs, & meta description etc. These settings will help your site rank higher in search engine for particular keywords.
I have been through all 3-sites and could provide a similar design, look and feel. However, I would like to discuss the TECHNICAL FEATURES of the projects with you. I would prefer a quick chat or a call to finalize all the things and get this started.
Let's discuss the project.
Thanks,
Salman