Would your son not be able to enter and leave the US on his UK passport? My dd has both as she was born there and we always went on the same passports as she would have had to que in a different line otherwise...
No experience of US here, but I have a non-UK EU passport, my kids have British passports, and have dh's surname (I have kept my own). I have found it useful to carry the long birth certificates with me when I travel, as some countries (Germany and Switzerland particularly) get a bit arsey about believing the kids are actually mine. (The fact that they all look like little clones of me is, apparently, neither here nor there).
DD1 (now 23) has a US passport and we are both British but we only travelled all together when she was tiny, so prob. not v helpful.
However, IIRC we did use her US passport whenever we left or re-entered, even though we only had GB ones and went through the aliens [wierd eyes emoticon] channel. (They never removed her for her own protection anyway.)