We just crossed back to the U.S. two weeks ago with our kiddos that I had lost one of their passports, the other one has never had a passport (by the way the border patrol has the ability to see if you have an active passport even if you do not have it with you, per my neighbor who is BP) I made sure to bring our birth certificates , we didn't have a hard time crossing (maybe because he could see mine and my daughters were active on file just not with us, we had other forms of i.d. and I dont believe there was anything suspicious about us) BUT that BP Agent was super cool and we all know it can depend on the day (heightened threat or word of illegal items going to be crossed) or the agent or the agents mood, he said the way to surely get no hassle is a. Adults have the passport for themselves , and B. With kiddos, He told me the most cost effective and easy thing to get for them is a state issued i.d. card and birth certificate. The cards (maybe the real passports too, we were just talking about the card passports since they are cheaper) expire for children after only 4 years so if you want to go back with them again after 4 years you have to go through all the paperwork and payment again until the are 18. Off to the dmv I will be going to that because I think the I.d.'s are $12 & don't expire until they turn 18.
I cross back and forth into Nogales all the time without the passport just my drivers license since I know they can Tell I have one but I do always get the lecture about needing o have one so, especially to be on the safe side with kids I will do exactly what the BP Agentt himself told me to.
Hope that All made sense and helps!