Honestly, I feel your frustrations and heartache. Not easy to handle 3 children and in law especially your youngest is only 5 mths old. It is hard to set a routine so that you can get some rest but somehow, it didnt work out.
My eldest, 5 yo, has been very trying too. She would be fighting, snatching things or shout loud loud to her bro. My mil is the primary caregiver with my helper. To stop them from making noise, she gives them gadgets or switched on tv. Very convenient way for her.
So now, I am using affirmations and reward stickers. Despite moments which she might be shouting or anything, I will find anything that is good (deaf to the bad). I affirm her and present her with a reward sticker (make it a great deal). Then i also strike a deal with her that she must not shout (for eg), if i check with mil and maid that she has been really good, another sticker. Accumulative stickers eg 5 will have a small reward. It works on my gal as it gratifies and stokes her ego. I cant change or talk back to my mil so I can only make my child change the way she behaves.