Overbearing MIL dry nurses and starves child, trespasses, fires the nanny, and threatens to call CPS

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I am a widower. I lost my wife (Anne 34) just minutes after she gave birth to our first baby (Sammy). She had a difficult pregnancy so I took an indefinite leave 3 months before she was due. Sammy's 4 months old now and before I went back to work, I told my MIL (Sandra 56) about my plans and if she can recommend a nanny to take care of my daughter when I work. She offered to do it (nanny) for free. I told her she's free to come by anytime during the day if she feels uncomfortable with a nanny looking after Sammy but she insisted on doing it herself. So I said yes and gave her a copy of the house keys. She comes 30 mins. before I leave for work, and when I come home, she stays for dinner and leaves after putting Sammy to sleep.

Everything was fine for the first couple of weeks until I noticed that Sammy's not feeding as much. Her formula's barely touched. I asked Sandra about it and why Sammy's not feeding well. She said she's trying to breastfeed my daughter. At first I thought she was joking then I realized she wasn't. She said Sammy needs to latch for a few minutes everyday to "activate" her milk production. I almost lost it, I told her she cannot do that, and she needs to stop. She said she will but I caught her again when I walked in my daughter's room and she was forcing Sammy to latch. I confronted her and told her she's no longer my baby's nanny. I didn't ask for the key back as she is still welcome to come visit anytime.

I asked for a 1 week leave from work to care for my daughter and find a nanny. I found one but two days after she never returned. I called her and she said my "Mother" fired her the day before. I asked her to describe the woman and I was livid when I realized it was Sandra. She came in my house using her key and fired my nanny. I was about to call her when she showed up and said a convoluted story like how I hired an incompetent nanny, etc. etc. I told her to leave but she refused and told me she's calling CPS because I am endangering my child. We argued back and forth before I called the police and she was charged with trespassing.

I know my MIL is grieving the loss of her daughter, I am too. But she crossed the line when she disregarded my wishes. She is very upset with me. My SIL and BIL are calling me ruthless and I am now second guessing myself. Have I taken it too far by calling the police? AITA?

EDIT: Thank you everyone for your advice and showing concern for Sammy. I called CPS to tell them about the situation. My mom is coming over to help look after my daughter and look at our options (she's a retired family law attorney). I do have a doorbell camera but reading some of the suggestions here, I decided to up my home security system. BIL and SIL know the whole story and they also think that forcing to breastfeed Sammy was wrong, but they are angry at me for calling the cops on MIL and having her trespassed. They said it was unnecessary and cruel to do to a grieving mother.

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freya
The brother-in-law and sister-in-law are siding with MIL, which probably means she only told them half of the story like a typical narcissist.

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BIL and SIL know the whole story and they also think that forcing to breastfeed Sammy was wrong, but they are angry at me for calling the cops on MIL and having her trespassed. They said it was unnecessary and cruel to do to a grieving mother.