The Kage meeting wasn't about any danger involving nukenin or rebel clans. We can tell by how lax everything was. Barely anyone cared that Naruto had been late, they were only bothered by it slightly since he's the one who called the meeting to Konoha. Not only that, but things are so peaceful that TenTen cannot sell any weapons.
They were either just chilling or discussing other forms of paperwork.
I don't see any reason as to why Naruto could not have taken Boruto with him. (His son will likely be Hokage after Konohamaru anyway. Might as well see how dad works early on.) Or made shadow clones as others have mentioned. Or ask Shikamaru to stand in his place of the meeting was so important, since he's more than capable of running things.
He could have even just said something different to Boruto instead of the basic "You'll have to deal with it, sorry. Not my only family. You're a shinobi and we endure." Something along the lines of "I'm sorry, you're my son and I want to spend more time with you as well. Tomorrow, I'll take a day off just for you. But, you have to behave since I have this meeting now." Something just to comfort the kid.
Then again, a conflict for part 3 is needed since Boruto is the main and the story can progress. Guess daddy issues are it.