The only time you can make a citizen’s arrest and be on semi-solid legal grounds is if you detain someone who is in the commision of a violent felony and you can make a good argument you made the stop to prevent further injury. Aside from that you’d be facing charges or wrongful detention, possibly kidnapping, etc. Detaining an illegal alient would get you in more trouble than the illegal would face for being an illegal (what am I saying? An illegal alien would not only NOT be punished, but would be rewarded for being an illegal!).
Accordingly, a sympathetic ICE employee (there may be a freeper here) could do the detention and arrest job, then. It should be done away from demonstrations, cameras, etc. Such as enroute, after tailing her for awhile.