As counterintuitive as this may sound, your best chance is actually to strengthen your chatot’s heart. You see, the advice Nurse Joy was giving you wasn’t because your chatot’s heart would explode or because getting excited would induce a heart attack. Rather, it’s because your chatot’s heart is currently weaker than most other chatot’s, and as such, a lot of exercise would exhaust her (or, more specifically, her circulatory system) a lot faster and put her other organs in danger due to restricted blood flow. However, there are ways to prevent this from happening, but it will take time and a few lifestyle adjustments for Chatters.
Nurse Joy should have given you tips on where to go from here, but it comes down to the classic diet and exercise technique. If you haven’t already, add more plant matter to your chatot’s diet. Consider greens, as well as certain seeds such as flax (ground, of course, to prevent Chatters from choking). Aim for foods rich in omega fatty acids, as these acids are anti-inflammatory in chatot such as yours.
Additionally, add a bit more exercise to your usual routine. While it’s not recommended to overdo it, a little extra exercise will help your chatot strengthen her heart and improve her overall circulatory health. Every day, have her flap her wings vigorously in repeated bursts of movement for as long as she can go. Have her fly about the house, and consider building her a small “gym” (this can be as simple as a climbable stack of books) that she can go up and down on foot.
Finally, if Nurse Joy gave your chatot a prescription, don’t skip a day. That goes without saying, but even the small things will help in the long run.
Again, these solutions will take time, but addressing her health issue rather than attempting to force her to rest is honestly the best way to go about ensuring your Chatters can get back on her feet, so to speak. As for the short-term, what-to-do-about-an-excitable-chatot part, my best advice is to increase the amount of time you spend with her in order to teach her that you haven’t abandoned her. It may be that she’s excitable because she didn’t think you were coming back (a common problem with house pokémon), so training her to understand otherwise will help her stay calm, even when she sees you again.