My guess is this: what she does not 'get' is that she is not the authority in the home which was once hers.
"We took there home over so it is our house but they lived here for previous 30 years. "
Wow... I can't imagine being older, being shuttled back and forth each week from relative to relative, and then, in my own home, my son's girlfriend is laying down the law with me. My guess is that this could be one way in which she is reasserting her authority in what she likely still feels is her own home. She may see herself in a matriarch position, however, you perceive her to be troublesome to your child's ongoing health.
The thing is, you are both right.
In my perspective, the Grandparent Privilege of feeding sweets only works when it's not the norm and not too often. For example, my folks do sweets with my son and don't always listen, but they only see Kiddo once in a blue moon. He's older, knows this is not the norm, is naggy for sweets for a few days afterward, and then all is well. In your situation, you are right, she is a near-constant presence for significant chunks of time and should be helping you feed your child well.
Here's where your boyfriend NEEDS to step in. Let me first say that I am not against living together before marriage or having a baby together in a committed relationship outside of wedlock. I did this myself and it worked out well(albeit -we were older and both previously married). That said, I have never doubted what my SO said about me to others, to his parents. Not for a second. So, if you are doubting his conversation with his mom ("But, I don't know if he's just telling her i'm weird about food I don't know what they're saying behind my back. So, I don't know if I have a nutritional problem here or a relationship one."), it's time to look away from his mom and take a hard look at your own relationship.
There are still options. Someone else could live in his mom's home and the three of you could still move out. He could have a good heart-to-heart with mom. The three of you could come up with a plan which allows her more autonomy in her former home. Personally, I think this issue goes deeper than a simple "she doesn't respect my wishes"... If it were me in this situation, I'd be looking for a better permanent solution where mom is not living with you in her own home. I'd be moving out into a place which was mine first, and then if she came to stay for a while, there wouldn't be this strange dynamic of Who is REALLY in Charge.
Good luck.