AITA for telling my neighbour his kid can't come into my house to see my cats even tho the kid thinks of the cats as hers?

Messy title, I know. This just happened this morning and I'm still shocked.

If you go trough my posts you can see I've adopted two beautiful cats. They were strays. I've been gaining their trust for MONTHS and finally last week i let them in. Saturday I took them to the vet and microchipped them and started them on shots/treatments, etc.

I live in a rural area with my fiancé. There's a lot of cats coming and going and people sometimes feed them.

Today my FIL was at our house working some things on the garden (it's actually HIS house but he says its ours) as he usually does. The main gate was open because he was moving stuff. A neighbour saw his car and stopped to talk with him. My fiancé and I were getting ready for work.

My FIL told the neighbour something like 'Yeah, they have taken two cats in blabalba I only let them bc I now my DIL is in charge' (he was joking around). So when we came out to go for work, the neighbour asked me about the cats. I told him which cats were and he went crazy.

He told me those were HIS CATS. I told him no, they were not microchipped or taken care of.

Apparently during February he and his family had COVID. They came to the country house to quarantine since it has a gaden and more space (like a lot of people do) and let the cats in for a while so the daughter could be entertained. They have a huge untrained dog guarding the house. The dog is let alone ALL WEEK and they only come on weekends and feed him. Police won't do anything, this is fairly common in this area.

When they went back to their old life they let the kitties out again. Now, I know why I didn't see them for a while. Apparently his 7 yo daughter got attached to them. I don't think the girl is an AH in fact I feel sorry for her.

After telling him they are not his cats bc the cats are not toys for entertainment he started going on and off about his daughter loving the cats. I asked him what if the cats got hit by a car? They wouldn't have known. I told him the cats are MINE as I take them in and took proper care of them.

He then DEMANDED I let his daughter come to play with the cats. I told him NO. My cats are not going to the garden (not unleashed and not until hey have all their vaccines and are neutered and spayed) and I'm not letting them in in the house. Then he had the audacity to tell me it's not my house. My FIL told him. to leave immediately since it's in fact mine and my fiancé's house. He called me an insensitive asshole and I called him a neglectful person.

So, I do feel sorry for the kiddo since she's none to blame but I don't feel comfy letting people IN at my house, let alone this person. He has no business coming inside. Not even if he would have asked nice. Although if he would have been nice I MAYBE would have think about letting the daughter in the Catio (once they are allowed in the front porch) for a while but I don't want this person on my property.

UPDATE.
Alright, I think I owe you an update guys.

First of all: My two kitties are safe and sound. They are going to be neutered and spayed very soon and they are happy and enjoying the indoor life. They don't even approach the door.
Some of you were worried about my neighbour trying to steal the cats but let me assure you they are safe. I think it's cultural because of how houses are built in each country but my house is surrounded by a garden and to access said garden you have to open a big iron gate and the fence is concrete. Then you have to knock down the door and you can't accesss trough windows bc the main floor is high and because they are secured with persianas, mosquito nets and bars.

https://www.cerrajeriacejisa.es/puertas-de-hierro/puerta-chapa-acanalada-P72G.php (The main iron gate is something like this).

However, he did came yesterday to apologize. I thought 'wow how unexpected'. But he wanted to ask If I'm willing to give one cat to the daughter. I told him 'no way'. I'm not separating them. I told him, if his daughter is so interested in cats, I can help her pick one at a shelter but my cats are staying. He finally gave up and left. I don't think he's gonna try anything because he can face jail time for trespassing so he was just being annoying and entitled.

You all were also concerned by the dog. I'm a lawyer and I know it's not illegal because the dog is fed and has water. It's not chained either so it roams free around their property. They go like once a week and leave food and water. The police won't do anything, and no association can do either. Believe me I've called the police multiple times because sometimes people let their dogs to walk on their own and they have tried to attack me and they haven't batted an eye.

We're not in the US and dog as a guarding system in rural areas are common. A lot of associations are trying to change this but, if the dog is fed up to vaccines and chipped, is legal. Police can't enter the property if they don't have proof the dog is being mistreated and since he's fed and watered they can't do anything. I know a lot of you will consider this abuse but according to the law it's not. There's a lot of dogs in a similar situation in the zone. I was surprised by your concern because I guess I have interiorized it. In rural areas people think that's normal, so there's little I can' do since I can't go around trespassing.