Hello frustrated Cindy,
I hope that what I write can be of some help for you regarding your MIL. If I understand correctly, she has now moved close by you. Does she live with you? Is she bringing her dogs over to your house and likewise you are taking your dogs to her house?
Interesting enough, MIL's are people too

I have also had a very frustrating relationship with my own MIL. A few years ago, when I became a MIL, I was determined to figure out this role and NOT have a similar relationship with my DIL's. What I learned is that you two don't have to be friends. There is respect for her as your husband's mother and grandmother to your children. There is a place for her to be part of their lives. If a MIL has a problem with her DIL, she talks to her son. So if I have a big problem with one of my DIL's, I speak to my son and he can talk to her and vis versa. MIL's are not your mother, you have a mother and as I feel, I don't need another mother.
With regards to your pets. MIL gets to do whatever she wants to with her pets. You do not need to change her. You get to do as you like with your pets and MIL does not get to change you. If this is difficult for your MIL to understand, ask your husband to please explain to his mother, that your dogs have special health needs and you have to limit their diet to keep them healthy to avoid liver, eye and skin problems, what ever it may be. Have him let her know that it is annoying to you to have her question how you treat your dogs. Now if MIL appreciates the way you are raising your dogs, than perhaps you will influence her to treat her own pets differently but it is NOT your place to change her. Isn't that a great relief!
I was the first to get a yorkie and my DIL, who I am blessed to have an amazing friendship with(thank you God!) had to have one like me. She wasn't able to afford to buy a puppy from the same breeder as myself and bought one from a friend. I warned her that she needed to feed her dog a special diet etc etc. She hasn't done that and her dog has lots of skin problems. When she asked me what she could do naturally for fleas and the skin rash, she did what I suggested. His fur is ok but if she fed him a better diet, he could look better. See what i mean. I let her know in advance of buying the puppy and then after she decides, it's up to her. She asked for my help and opinion. We aren't guaranteed the opportunity to voice unsolicited advice and we certainly are not given the right to control or burden the other person with what we would do because we feel our way is better.