First off, thank you for your time.
I decided to go for a very user-centered and minimal concept with an oversized feel. I wanted to get to as few clicks/taps as possible for the user from the get-go. Then I decided it might as well be responsive to keep things interesting and more useful. I also decided to add a tab mechanism to allow more room for a user to concentrate on each scheduling situation.
I need to mention that unfortunately I didn't understand what was meant by the direction, "Allow the user to pick from a set of dates." I spent some time deliberating if this meant a range of dates on a calendar grid, or a pre-defined set of appointments with heros, or a come-every-x-day at 3pm sort of thing. For the sake of sleep, I opted for the weekly schedule option which fit into the tab concept nicely.
The whole widget updates via vanilla and jquery javascript. Also the page is using bootstrap 3 along with one of the brand fonts and the brand colors I found here.
I honestly haven't ever built a date-picker by hand (normally I would use a plugin or extend the jquery UI datepicker due to time/budgets.) It could have more enhancements, and better responsiveness on touch devices. It could also use a minus button on the planner tab section in case a user added appointment blocks... and then decides to delete it. Also, I did not do any validation yet. I did however go ahead and set-up everything as inputs, and made the pages submit so you can view the data hand-off.
All that said, it needs to be tested with real users. Especially if the users are on the elderly side of the population. It can never be too-easy ;)
I put a good chunk of time into this to make it from scratch and to execute it responsively. I did have some trouble with taps registering on mobile iOS devices for the dynamically created elements, but after some searching around I found a way to get the events to register as expected. Overall, this took me 7 hours, with around 1.5-2 hours on research and debugging/patching the iOS tap issues.
Thank you again for your time, and if you have any questions, please let me know.
Cheers! -- Matt McT