Activate visa status = equals being admitted into the US (entering the US on that visa).
Since that visa is subject to a 2-year HRR, then you are better off staying back since you’re the DV selectee. If you get scheduled for an interview, you attend that interview with your 2 kids without your husband, since he would have already entered the US with his J1. Once you settle down in the US, you look into sponsoring him for his own GC. He will need to obtain a waiver for the 2-year HRR of course, but I think you guys will have enough time to take care of that.