I know I am late in responding to this but I did get a passport..I did see on the application any former names and my maiden name and my maiden name also shows on my daughters birth certificate which I was going bring just in case but that info doesn't show on the passport but was on the application for the passport so how do they bring up this info from my passport?

Lucky you. Tried multiple times to get a passport at the post office. every time they game me a different excuse for someone not being available to take the application. What a waste of my time. I just said forget it. Will save the 200 bucks for now and get one when I absolutely have to.LOL

I would just like to say.. regardless of who has custody of the child- you must have on you during check in- a letter that states the Father is aware that the child is traveling to Aruba with the Mother and provide the dates, etc. The letter must be notarized and written and signed by the "Father". I have a son by a previous marriage and we travel 3-6 times a year, always International travel, and we must always have this letter. Please take one!

Any information you can give me would be great as I am doing the same thing and I found out I need a notarized letter to get the passport, but my concern is now I have her passport with a different last name will I still have problems through customs? Will just this letter be sufficient, or will I need to have more documentation other than Birth Certificate, Divorce Papers, Passport, etc? I am more paranoid and am on hold for 30 minutes with Homeland Security to find out. Let me know what you had to do and any advice would help.

If one of the divorced parents has sole custody, all you need is what's called a "Sole Custody" document. If you don't have that, you will need a notarized permission form from the other parent to take the child out of the country. It would be easier to get the document so that you don't have to get permission every time you travel internationally.
Even if customs doesn't consistently ask for either of these documents, you can bet that the time you don't have one, they will ask for one! Don't risk it!