Think about it, if you really cared about something and you let your partner knows, and he just said, oh you'll be fine, and went on doing the same thing, how would you feel? I would find it quite disrespectful. If I'm being unreasonable, I want him to convince me, not to just dismiss me.
My husband has gone and done things before that I preferred he didn't do, and made sure he knew it. Maybe I preferred it simply because I missed his company, and wanted to do something with him. Maybe it's because what he was doing was risky. He's had back surgery before and if he damages his back again they may have to fuse his vertebrae, which would limit his mobility, and from there maybe affect things he can do around the house or how he can play with our child(ren). But he still likes to play (American) football, go caving/spelunking, or do other stuff, with all carry the risk of something like that happening again. He knows I am worried about his back, but I can't make the decision for him.
Forcing or guilt tripping him into staying home with me or spending all his free time with me most likely isn't going to result in him being very happy, so our time together will end up being a reflection of that, and I won't be happy either. If he decides that he still wants to do whatever it is, I just make the best of it. Invite a friend over, or order a pizza and watch whatever movies I want, eat chocolate for breakfast, etc.
If any of us women really wanted a week off to go to the beach and sip mojitos with our mom & sisters, or a bunch of girlfriends, leaving the baby with our OH/DH... how would this thread be different? If we were posting that we REALLY wanted to do this, and it's been an annual thing before the baby came along, but now OH is saying we're being unreasonable as the trip falls on his birthday, or because he's never been alone with the baby for that length of time, what would the responses be? Probably more along the lines of "Well, you need your own time to be who you are! He's the dad of the baby, tell him to step up and parent! Go have fun! You shouldn't be expected to give up this part of who you are just because you have a baby!" Or if it was already booked and the mom was feeling guilty about leaving, it would be "Well you've already paid for it, go enjoy yourself! Your OH will be fine!"
The OP has been given several great suggestions as far as how to deal with this without having a knee-jerk end the relationship reaction. She can find out if there's a way to go along. She can come up with her own things to do throughout the week with family or friends. If she's feeling worn down and needing her own time, she can set aside her own weekend or spa day or something and let OH be on dad duty for a while.
I realize the situation isn't ideal, but since her OH basically said he wouldn't be going anymore if he hadn't already paid for the trip, I think it's healthier for the relationship for the OP to just move forward and make the best of that week. If he booked Jan 2015's trip without telling her, after all this? Well, then, that might warrant some other action.