Legal Question in Personal Injury in Michigan

It does not sound like a strong claim by your neighbor if all you do is walk past his or her house with your dog. A trespass can only occur if you (or your dog) enter your neighbor's property. There should be an easment on your street that allows you to access to and from your property. Your neighbor does not own the street.

As for the nuisance claim, I don't see how your walking past their house interferes with their quiet use and enjoyment of their land or how it causes a danger to anyone. Obviously if your dog was vicious, you did not lease it and caused them to retreat to their house every time you went past that would be different.

I would suggest allowing your dog to enter their property (especially to go to the bathroom). Besides that as long as you leash the dog and follow common courtesy (not allowing it to bark, scare anyone, keep it under control, etc.) I do not see any problems for you.