I have spoken to DH about not backing me up and his reasoning is he's never had a baby before so he has no idea what's right or wrong. I have tried to tell him there's nothing wrong with how I'm breastfeeding but it seems he believes his mum over me since she's a nurse.
Perhaps say to him that every new parent goes through the learning process, and if he feels unequipped to decide what's okay and what's not, the best way to give himself confidence in parenting may be for you both to attend a parenting course together, read some modern books on parenting together, attend a breastfeeding workshop or for him to come along to a few appointments with your other medical advisors.
Be clear that you're not putting down his mother but the current advice you're receiving/information you're reading is at odds with what she's saying. Sometimes people can get stuck following outdated advice because that's they way they learned to do things, and they don't understand that the science has moved on.
But regardless, while you are open to hearing her advice and suggestions, you're not open to being insulted, which is what she is doing. If she wants to make polite suggestions, you'll listen and consider them, although at the end of the day, this is your child and you will make the final decision. But what you won't accept is her speaking to you in a denigrating and disrespectful way like she is doing.
Try to separate the issues of 'being open to advice' and 'being insulted'. While your partner may not necessarily agree yet on the best approach to feeding you want to follow, can he at least agree that if your MIL is going to offer advice, it needs to be done in a respectful way? He may not have much experience in standing up for himself, let alone anyone else, with her.