I too want to welcome you to the forum.
Pamela has written a supportive and helpful reply .
I have been a mum with a young baby coping with a mother and mother in law but not permanently and now I am a mother in law.
You are coping with a trick situation that has both mums staying with you. I am wondering if you could get both of them to help you doing things you are ok with them doing. maybe all four of you may need to sit down and work out a plan with guidelines and boundaries with everyone listening . . As Pamela mentioned working out house rules is a good idea.
I thinking having the two grandmas argue is not good for you or for your baby. Maybe if you can explain to them how their arguments affect you but you know they love you and your baby.
How do you think you can make this work ?
Does your mum and your mother in law help with cleaning and cooking?
Having a baby makes one tired and sometimes nervous, you have a lot of support you just need to communicate with them to work out how you can all live together.