I do not know the laws, but investing in a home AED in this situation is a wise decision. The cost is nothing compared to the loss of a life in your home on your watch. I would definitely buy one. And check into ADA and other possible state and federal tax credits for purchasing one. I know there are many such credits and incentives for such business purchases.
Here are some links for you to read. I’m not sure what the requirements are for in-home fitness training business because they are not clear. However, if you do operate from your home and you are AED certified, I would definitely purchase one and have it available for when/if that moment comes. You should talk with an attorney. I operated a mobile personal training business in the Chicago area for many years, but I was not required to have one with me.
I hope this helps.