Homepage division

So, a bit of a weird one. I am not sure how achievable it is.

I have 3 different websites which I would like to host under the same domain yet have their own navigation.

I was wondering if it was possible and if yes, how, to set up a simple homepage that would have 3 picture links on it and only that. Each of those links would take you to each website.

To be more specific, I own the domains ADgrimaldi.com and DTBDproductions.com and another one that expired called SAtraining.com

I’d like DTBDproductions to be the main domain and then have 3 as sub domains ADgrimaldi.dtbdproductions.com, production.dtbdproductions.com and footinthedoor.dtbdproductions.com

So when someone goes onto DTBDproductions.com they get a page with 3 picture links to those 3 subdomains and when they navigate on each of the website, they stay in that sub domain area.

Sorry if this isn’t clear, it’s not an easy one to explain.