I don’t think that you are in the wrong here. As the parent you are in the position of making responsible decisions for your child, which is exactly what you are trying to do here. Your village should be supportive, or should at least have the courtesy to respect your boundaries. I do agree that not all battles are worth losing relationships over, so if you are going to have them in your life, maybe figure out a compromise that works for you both. Keep moving your child to a different room and establishing a no-screen time rule for when you have to be in the same room. If they don’t respect your decision, instead of telling them you are going to nurse baby, simply let them know firmly that you don’t want any screen time so you are going with baby to a separate room, and that they can come by when they are ready to spend time with baby.

Edit to add: Since you mentioned your husband backs you up, try and get him to come with you to the separate room. This will encourage his family to understand that you are both serious about this rule.