A lot of your characters will need to go for a checkup at Hibbert's Family Practice before he decides he could charge them more money in a hospital. I think he triggers a few of the checkups himself, but a lot of them are triggered by the characters themselves. (If I remember correctly.) So, just watch for the exclamation points and send everyone in for their check up. (I recall it taking a couple days for everyone to trigger. Don't stress about it; Count Burns is a permanent skin, so I'm pretty sure you can always do his questline.)
Go to the FAQ section of the forum. The last pinned thread is titled something like "Complete walk through and Guide". It is an AWESOME resource for exactly what you want. It even tells you which characters to have free at a given moment, so they can trigger the task. Start by reading the Hibbert section there, be sure you did all those steps, and then move to the next step.
Try it. You'll love it!
USA/UK Race To Throw Country Into Utter Chaos = TOO CLOSE TO CALL
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Go to the FAQ section of the forum. The last pinned thread is titled something like "Complete walk through and Guide". It is an AWESOME resource for exactly what you want. It even tells you which characters to have free at a given moment, so they can trigger the task. Start by reading the Hibbert section there, be sure you did all those steps, and then move to the next step.
Try it. You'll love it!