DNS non Dreamhost domain name

I have a school’s site at glendaleinfantschool.com. That domain name and the Wordpress site is all fully hosted at Dreamhost.

The site actually needs to respond to www.glendale.warwickshire.sch.uk which is controlled by that school’s education authority. They will only redirect the web traffic, email etc. will stay where ever they are now.

I’ll guess that the most robust and simplest solution would be to add their own unique IP address, as they are currently on a shared hosting plan at Dreamhost.

However, are there any other good solutions? What will I need to add to the Dreamhost panel and what will I need to specify to the education authority?

The simplest would be to ask the education authority to add a c-name from www.glendale.warwickshire.sch.uk to glendaleinfantschool.com, but then the site would be responding as glendaleinfantschool.com.