Don't let any of these responses get you down or make you sad, especially the rude and obnoxious ones. Everybody's situations are different, so you shouldn't be judged for that. All you're doing is sharing your experience.
You did absolutely nothing wrong whatsoever. First off, I completely understand what you went through with regards to your son, as I have had first hand experience with my son throwing up in a restaurant. At least you were nice enough to alert the waitstaff to inform them of the incident. Some people wouldn't think twice about it or even care about the welfare of other diners around them being effected. That was very considerate of you. Even though your waiter wouldn't technically be the one to clean it up, he should have gotten someone who could clean it and not just have shrugged you off.
Second, it is a known that at the CRT, they do provide kids under 3 with a meal whether it be some french toast sticks or noodles for breakfast/dinner. The waiter should have been a little more attentive and brought something for your son. When we were there back in December, my daughter was 2, and our waitress asked specifically what she'd like. I told her that she was 2 and she told us that it didn't matter, that she'd get her whatever she wanted. She brought her eggs and french toast sticks. So in your situation, I think you just had a not so great server. The milk thing can go either way. He probably just thought you needed some for your coffee, big deal.
Lastly, yes, I would be annoyed if I went out of my way to order a special dessert for my kid and it was forgotten. Especially if the other tables around you were getting the proper attention. It would have annoyed me and yes, I'd be pissed if my husband left an additional tip for such lousy service.
I'm so sorry you had a miserable experience there. Hopefully one day you can go back for a better time