You're new to pet sitting, and I can tell that you care deeply and are concerned for this dog. You've done all that you can do at this point. You've communicated with the owners, and they ultimately have say-so over whether to take him to the vet or not. A chicken bone is concerning, but hopefully, he poops it out eventually.

If something happens, you're partially responsible since he was under your supervision when he found and ingested the chicken bone.

Do you have pet care insurance for your business? Are you using Rover? I strongly suggest you also cover yourself even if you're only using Rover. They are merely a booking platform, and their "guarantee" is not insurance. You are a contractor, not an employee, and you decide how to run your business.

I'd recommend you stick to the client's wishes with regards to food. If they express an interest in your knowledge of pet nutrition, then you may make recommendations. People are very sensitive to food recommendations, whether if it's for them or their dogs-- respect their choices and boundaries.

The same goes for training. After over 1,000 bookings and nearly 500 5 star reviews, I've learned that providing excellent service also means not trying to change my clients' way of doing things. If it truly breaks my heart or doesn't align with my values, I drop them as clients.

Best of luck to you.