As a dual citizen, i have had very little issues dealing with the army. My parents moved back when i was was a toddler. Any time I went to Israel before 18, I had no issues as long as I brought my Israeli passport. Upon turning 18 i needed to obtain a new Israeli passport. As I was a dual citizen living abroad, I was granted a status that allowed me to live in Israel for up to a year, as well as visit for no longer than months at a time. When i went to learn in Israel, I applied for an extension (with a letter from my yeshiva), and I was granted a two year extension. When I returned married, i made sure to go in a separate line than my wife (my original extension was still in effect.)
I have been back a number of times since and have yet to encounter an issue.
When I iy"h go back with my kids, i will have them go in with my wife so they don't have to deal with all these extra steps, especially if they would like to live there long term.