I need a professional redesign of a clients website/s

My client currently has 3 websites - all are pretty awful. 2 are WP and the other is custom built (using PHP) with a very complex back end system that they are terrified of meddling with because they run their training programmes/make their money with it. Before we tackle the back-end, I’d like to merge the 2 WP sites (possibly with a new URL) and significantly improve the design and make it better for SEO - and I wonder if it’s possible to link the custom back-end into the new WP site for now?

The current WP sites are: https://www.private-paediatrician.com/ And http://www.clinical-training.co.uk/

I’m looking for project costs and availability, please.