How do I deal with feeling like my wife and child don't care about me on "special days"?

First off your wife sounds like my husband.  You need to communicate to her how you feel about this not just the lack of gifts but her behavior and tell her what you need.  She may or may not change her ways, but you need to give her a chance and remind her.  Sadly if she doesn't change you need to buy yourself something and do something for YOURSELF.  Also STOP giving her gifts and cards and and if she asks "he did you forget...." just put it back on her and tell her what she usually tells you and never follow through.  Your daughter, sad to say sounds like she is taking up your wife's habits in this regard.  You can still correct your daughters ways and you can tell her how you feel too, when she doesn't finish and follow through with a gift or card for you or anybody else.  Luckily for me, my birthday falls the month before my husband so if he puts forth no effort then what goes around comes around, but i'm still a bit more thoughtful then he is.

***Also, you're not her father so don't expect her to get you a gift.  Just like mothers day she isn't your mother, you don't need to buy her a gift or take her out to eat that is on your kid(s) even if small.

I hope you don't make a fuss over her on her birthday etc. If you do - STOP. That's how I handled my (EX!!) husband who took great delight in giving me less and less for my birthday. I ended up giving money to the (older) kids to buy me something - and they loved doing it. If I felt like going somewhere, I'd organise it. If ex wanted to come along fine and well, but I never made a fuss about him participating. I don't like your wife who is treating you as a meal ticket - not the love of her life. And that is something you should never have to ask for. If you do? Move on before you lower yourself to begging!! BTW - your child is only following your wife's lead. Stop that in a hurry, or you will be treated like that for life.

maybe you should talk to your wife about it, she might think thats the way you want it

Start by acknowledging that you're a fully grown adult and as we age we're supposed to accept that we won't always be the center of attention. Instead of just waiting for your wife to organize your birthday (like she's your mom) be proactive and suggest activities you'd like to do. You appear to be taking a very passive role in all of this. 

My goodness.  Your wife asked you if you wanted a birthday party and you declined.  You want to go to the theme park?  Pick a date and go with the family.  My point is that you need to be more specific.  If you want a birthday or Father's day gift, tell them what you'd like to receive.  If you want a party, schedule your own.  Perhaps you're giving the impression that you don't want to make a big deal about any special occasion.  

Best action you can take for all involved is to sit down with your wife and tell her how you are feeling.  Share your observations of her behavior and that of your child, and explain the emotional and mental impact on you.  Tell your wife you do not feel acknowledged or celebrated, and ask her to share her perspective.  If you feel there is no equality in this relationship, tell your wife and enter into honest conversation about the dynamic between you.  Also, think back over the years.  Has this behavior from your wife been recent or long term?

I would definitely sit down with your wife and explain honestly how you feel. It seems to me that you feel like you are being not celebrated and that can be hurtful. Let them know that you do appreciate gifts and birthday gatherings on the spot rather than later. Don't worry about it though I would just talk about it.

Have you talked to them about how you feel? Maybe when you told them you don't want a party, they thought perhaps you are not too into celebrations, etc. try talking to them about how it hurts your feelings that you are not celebrated in this family and it's making me a type of way. 

If you already spoke to them until you are blue in the face, what I would do is start celebrating yourself. When your birthday comes up, (if you can get off work) take a long weekend and take a small trip. When they ask why they can't come along, let them know that seeing how no one wants to celebrate me, then I'm going to show myself a good time with friends or do something you really enjoy without them. I think they'll get the hint. 

Is this a recent change or have you been dealing with this for decades or...?

What you described and all that it implies is a nightmare scenario tbh, I'm not exaggerating. Can you talk with your parents/siblings/friends about it? I don't think there answer here is that you "deal" with your feelings, the answer is you deal with the situation. How you do that is something your parents/siblings/friends can best advise on as they know both you and your family, and we don't.