It makes perfect sense. You are torn. And I think BIL counted on that.
I don't mean to be alarmist, but I do see a HUGE problem. Your DH has shown that when push comes to shove, he will choose his brother over his wife/kids/marriage. His brother is a master manipulator and you are outmatched. Logic and reason have gotten you nowhere because your BIL has your DH's heart in his hand. At this point, even if your DH swears your BIL will not stay in your house, you will not be able to believe a word he says.
He has bought into your BIL's "I'm so needy and a victim of circumstance" speech and sees YOU as the enemy now. YOU are out to get his brother, just like all the other unreasonable people who won't support him financially, such as the horrible roommate of MIL who dares to ask he pay 1/3 of the rent. It's his brother against the world and he is firmly on his brother's side now. IMHO, I see this as a much bigger issue that whether to go on vacation or not, or whether to fund a week's stay at a hotel.
That is why I (just me) would cancel the vacation. One, I wouldn't want to spend time and money going someplace with a husband who will cuss me and never blink. Two, the vacation is a piddly concern compared to the real issue, which is that your DH has lost all the progress he's made over the years and is treating you with zero respect because his real loyalty is to his useless brother. The BIL is no longer your main problem...Your DH just graduated to that position.
Your BIL has already won, at this point. He has turned your DH against you and made you the bad guy. He has just won another convert, who has a job and can house him and pay his bills. Life is good for BIL and DH gets to feel like a hero. This is why I would die on this hill. Either that, or get used to being an ATM and hotel.
You're not me. It's your life and you have to live with what happens, not me.