Whoa. First things first: If you don't deal with the "mandatory vacation" thing right now, you are going to end up spending a wad on a vacation that will make you miserable -- and will strain your fairly new marriage, too.
Please deal with this before you go further worrying about the lack of birthday interest or discussions of your home choices or your money. Seriously, the vacation thing is a huge, waving red flag.
Does your husband go along with this idea? Does he agree that yes, you and he MUST take this particular vacation with his parents? Did HE get a vote or say in the destination? Does he expect the two of you to pay your own way or (worse) does he know mommy and daddy will pay for you both (thus giving his parents the "right" to feel they run the whole vacation, if they pay for any of it for you and him)? In other words, where the heck is he in the vacation discussion?
Have you taken these can't-say-no vacations the past few years of your marriage? Did you want to? If not: Why did you do it?!
If your husband is so tangled in the apron strings that he cannot say "I am an adult in my own marriage and want a vacation with my wife, to be a couple, not with my parents" -- then you married mama's boy and need to sit down and talk about what the term "man up" means here. You have a right not to spend your family's money on someone else's good time. You have a right to have a vacation with just your husband. If htat is what you want to do, you need to tell him. If you went along with previous mandatory vacations, you unfortunately set a precedent that you agree that you will vacation with his parents; time to break that pattern or you'll be doing it forever. Do it nicely but very firmly: "This year we are having a vacation as a couple so we will not be coming to Europe with you." Period, no discussion, no debate, no caving in to weeping or sniping.
Oh, and HE has to say it. Not you. Him. If they accuse you of putting him up to it and denying them their "family tradition" of a vacation -- smile sweetly and say, "I know you'd appreciate the idea that Son and I are building a family tradition of our own" and change the topic.
But if he can't do all that too, it may be a lost cause.
The rest is related to all this, you know. Has he ever told them your birthday? Are you sure they even know it? He should, before the next one, tell them the date and be very clear that you would really welcome a card. And he should repeat that one week and again one day before the birthday. It's not really a big deal in the end, but if it matters to you, he should make some little effort with his parents. And he also is the one to nip talk of finances in the bud (mostly by keeping his mouth shut about his financial worries around mom and dad) and the one to back you up on any talk of where to move (again, do not discuss in front of them, ever -- let them know your new address after you sign the papers and don't ask for advice or even mention it beforehand).
Sit down and think hard about his relationship with them. Is there a pattern of his just doing whatever keeps them happy even if you don't like it? Does he know, though, if you are unhappy, or do you just say nothing? You do NOT want to turn this into "it's me or them" but you also have to be assertive if you have a mama's boy or a "go along to get along" person in your life.