I suspect drugs are involved here. Not because she's in an abusive relationship, and not because she is facing homelessness, but because of her nonsensical arguments.

When I had a friend who had a son about the same age, just under three, she had me help her escape her abusive husband. Don't get me wrong, he was an asshole. However, she was back on drugs and was lying through her teeth about it. She made circular arguments like this that made absolutely no sense. She hyped up her victim status, adding more and more embellishments to her husband's behavior. I have no doubt that her husband was a bad man, and I blame his abusive, controlling behavior has the thing that ultimately brought her back to drugs. However, in hindsight, I understand how much she was blowing things up, exaggerating, and lying. The drug use was also making her paranoid, hypervigilant, and skewing her perceptions of reality.

The question here shouldn't be "how can I keep my 3-year-old entertained in a car all day", but "how can I keep us from living in our car". Blows my mind that she has made these assumptions, without even consulting a lawyer. My friend also refused to follow legal advice, and kept lying and trying to manipulate the system, and trying to get people to believe her as a victim. Ultimately, she permanently lost custody of her son. I am not in touch with her anymore, but I know that her husband has full custody and she has visitation rights, and it has now been 5 years.

OP, if you read this, for the love, talk to a lawyer and follow their advice. At least make a post over on r/legal. You are saying things, and making assumptions about the system, that just simply do not make sense. It's like you're getting all of your understanding of the world from a Lifetime movie. That's why people are having a hard time believing you. No one can understand why you would leave home and shelter with your parents, to come live in your car with a preschooler in a Massachusetts winter. If a lawyer tells you it is in your best interest to do so, well that would make that decision make a lot more sense, but to assume that is your only option ( regardless of how bad your ex is, and whether or not he has connections to police) without finding out whether or not that is true is ridiculous. At the end of the day, police actually have very little say over any of this. Custody is determined by the courts, not by police. The police cannot actually legally take your child from you, without a court order, and even then DCF would also be involved. I know this for a fact, because of what I went through with my friend. Also, my father is a lawyer. It doesn't matter how many friends he has, unless they are all willing to give up their careers, the police are not just going to come in and take your kid. That is just not how it works. Now, he could take hold of the kid and refuse to give the kid back to you, and for the same reasons, the police could not take the child away from him. He is the child's legal father, and without a court order, the child cannot be removed from his custody. That is how my friend lost her son. Her husband showed up at their house, and took their child, and she never had custody of the child again. Granted, he took the child while my friend was high on drugs, and my friend lost her child because she couldn't pass a drug test. If my friend had passed her drug test, and hadn't been actively using, the courts would have worked out a custody order, and she would have had shared custody, or perhaps full custody, because her husband was no Peach either. That poor kid. He really got the short end of the stick....