Make an appointment to speak with the head of that precinct, take in all the evidence you have on your stalker being your stalker, and show it to them. Ask if it is common for their officers to take the word of someone with a pattern of law breaking and obsessive behavior over that of their victim. In the future- though I would hope there isn't a third time- if someone breaks into your house, DO NOT ENTER IT. If you see signs that a break in has occurred, call the police, have them come out, and wait in the yard in your car, with the doors locked and windows rolled up. Wait until the police clear the house. Entering a house that has been broken into puts you at risk of the burglar still being there and being directly attacked by them.

Wait, you have to contact the person you are filling the restraining order against? In the US, at least in Florida, the person is "served". In cases like this, and in domestic violence cases, law enforcement will serve the papers for you. See if anything is available by calling local non-emergency.

Well, that’s no fun! A restraining order only encourages a stalker to keep trying. The way to get rid of a stalker is to date him. Make sure you smell bad and are boring on your date. Order the most expensive thing on the menu and don’t even touch it. He’ll leave you alone and pass the word among the stalker community.

This is called the "letter of the law". If you do not have an actual restraining order then you are technically harassing him by informing him you are getting one. It's shitty, but people lie and I'm assuming that you never called the police either time he broke into your house.

If I were you, you should take a few self defense classes and maybe get a weapon or two. This guy is not going to stop and restraining orders go only so far.

Plot twist: The stalker made the call to the police from inside your home.

Narcissists and sociopaths are crafty beware.

With a restraining order in place the stalker should have been automatically arrested for breaching it and as such, you should put a complaint in against these officers for not doing their duty (if you showed them the order).

Ignore me, I misread the story. Get the restraining order before making the threat of one.

Unfortunately quite a lot of stalkers, harassers, and abusers make a study of the law and are quite familiar with exactly how far they can go without inviting action by the police. Honestly I'm surprised you didn't file criminal charges against him for trespassing, burglary, or breaking and entering after finding him in your home uninvited.