If you want to save your marriage, yes it's unreasonable.
Please don't let a bunch of strangers on the DIS goad you into saying or doing something that will make this situation worse than it already is. {{hugs}}
I agree with this.
A lot of people are saying "this is the hill I'd die on." But, really? What does that mean to you? How far are you willing to take this? Up to divorce?
Your DH is not being nice & not taking your feelings into consideration & going back on what's he said. He's choosing his brother over you & your kids. I get that. I'd be ticked. I'd also feel incredibly hurt, especially after he called me a name. You absolutely need to discuss how he's treating you & making you feel, & you deserve an apology.
But, sometimes, you just need to take a step back & take a deep breath & realize, it is what it is. You can't change anyone else's actions and reactions - only your actions & reactions.
Your DH is not taking your feelings about this into consideration, but are you considering his feelings? Sometimes, it isn't about who's right & who's wrong. It just is - the situation is just the way it is. As much as your house is your house, it's your DH's house as well. You're partners. You're on the same team (even if doesn't feel like it right now.) He gets a say. You can't force him to say no to his brother. You can tell him how you feel. You can give him advice. You can tell him you strongly wish he'd consider what you're saying & how this situation affects you. But, at the end of the day, he has just as much right to let his brother stay as you do for saying he can't stay. It's his house too. So where does that leave you?
You can't change or cancel your vacation.
You don't want your kids to be sad while they're on vacation.
For the record, I think you're right, & I'm on your side. But I think it's a lot easier for us here on the internet to say, "I'd say no! There's NO WAY I'd let him stay at my house. I'd make my DH stay at home too!" than it is to actually be in the situation & be living it.
I know me, & I know I'd probably cave for the sake of my marriage & for the sake of the family vacation. However, I also know DH & I know that he wouldn't put me in this situation & he's never cursed at me either.
So I guess I don't really have any good advice... just don't let what is said here get in your head & end up making a bad situation worse.
The idea that the brothers grew up together in a difficult situation and therefore are close and want to have one another's backs is a nice idea. But BIL clearly has no interest in making sure his brother is happy. He's been told NO a hundred times. He's continued begging DH. I find it extremely difficult to believe that he is unaware of the strain this is putting on you and your marriage. But he's not concerned about his brother's marriage or his sister-in-law's feelings. All he's concerned about is getting what he wants, when he wants it, regardless of what it costs anyone else financially or emotionally.
He is not homeless. He will not die on the curb. He wants a vacation in your house and, like a child, if he's told no he'll throw a hissy-fit and sleep in his car. If he is pushing this hard just to stay there for a week, I see no reason to think he's not going to push even harder to stay for years.
You have a few days before vacation. If I were you, I'd try very hard to find a counselor who might be able to talk you two through this crisis. No one can fix a marriage in a session or two, but someone may be able to help you through the current disagreement.
You're worried about your home. You're worried about your pets. You're worried about your marriage. No one should be treating you this way. Talk to DH. But push aside the anger and let the fear, the disappointment, the pain and the stress show. He needs to understand that you need to be taken care of as much as his brother does. Another thing that maybe a counselor can help him see.
I also agree w/ this as well.
If you do decide to not push it any further & your brother-in-law ends up staying at your house, maybe you can try to make counseling one of your "conditions" - "I'll agree to this if you agree to counseling" kinda thing.