Would it be wrong to tell a friend that her dog needs more exercise?
That depends. What's wrong with your friend's dog?
She's such a bad trainer and the dog is always sick. I want her to take more responsibility.
If you see that an animal under your friend's care is suffering, it's ethical to advocate for them and ensure them a healthy life. Your friend will thank you later for holding them to an ethical standard in caring for their pets.
I doubt she will take responsibility, but I'll try to convince her to.
I think you are making a good decision! Making sure that animals and pets are well taken care of is a good thing to do. Hopefully you can convince your friend so that the dog can be in better health soon.