Darn. If I'm reading your inquiry correctly, you're wanting to change the first page (the direct link), not the second? If that is the case you can create some images that contain the date/time/age which you can then link to the appropriate event info. Then, put them in columns next to each other. Keep the colors of the date/time/age consistent for each link to help your customer choose other clinics for their child to attend. They'll look more like buttons this way.
@Patterson - Editing to add that I've been playing around (because your question intrigued me). This link is based on the Bedford (7.0) template which doesn't offer the calendar style either (rather, it's a blog style). However, I think you could probably do the same.
I created an Events page
added an event
set the start day/time and end day/time
added a title
added a description in the content area
then inserted products that we already had set up for this client, but imagine each product for the age/time-block for each clinic and or camp.
in the Options tab, I set the thumbnail image
https://www.lossoflifeadvocates.com/new-events
