People don't throw themselves a baby shower - it's always given by someone else. That makes the requests for gifts NOT seem selfish. Also, showers are usually given much later in the pregnancy, when the risk factor of miscarriage is gone and the mom (or couple) is really in need to supplies. The mistake she made was putting registry info at the end of the invitation, which is what she regrets.
It sounds like you got so excited that you jumped into the planning part without consulting her. You not only figured out a gift, you started looking into games and decorations - which kind of took over the hosting role from her. Though you did not intend it this way, she may feel it puts more focus on you and your creative/organizing ideas, and less on her. This also compounded her embarrassment about appearing to request/expect gifts.
I think you should put your cute diaper cake in the closet and wait until she is 7-8 months along. Then YOU plan a shower (with her consent) or work with another friend - see how your sister and brother-in-law feel about a coed shower or a women-only shower. She may feel very differently when things are getting closer and she is more used to being pregnant.
If she doesn't, you can give her the diaper cake as your gift. For now, just go to the BBQ as a celebration and don't bring a gift. It's very early, and no one will question that her own sister isn't bringing something. Bring a "congrats" card and that's it. Be excited and happy for her - this is THEIR celebration and not something for anyone else to take over.
I think you are overly upset because you really are excited for her (a good thing) and you want to exercise your creativity (a good thing) but you know you kind of took over here (a bad thing) and you are conflicted. Swallow your pride, suppress your own emotions, focus on HER right now, and let the BBQ be THEIR day. Just let everyone know how thrilled you are for your sister, how exciting it is for your entire family, and let the hurt feelings slide away. There is plenty of time for emotion later on!