Split an existing website

General information for the website: We sell services
Kind of development: Customization of existing website
Description of every page/module: Please do not add me on Skype yet - Let's talk on pph first.

3 Colours Rule is a creative agency and a fashion training.
Unfortunately, the way the website has been developed is confusing visitors.

So I would like when people get on the homepage they choose if either the creative branding agency or the fashion training division. Then the website layout remains the same.

If you click on fashion then you don't see anything with regards to branding
If you click on branding then you don't see anything with regards to fashion

Very important: the website links need to remain the same as I have spent a lot money on SEO and my fashion keywords are doing very well.

So please guide me through what you would to undertake this task.
It's wordpress website. I also hope this will improve the speed of website which isnt great.

Thanks
Description of requirements/features: Same as above
Extra notes: