The rage could be a combination of things. One the change (divorce) the other is that an adhd child tends to take up alot of the parents attention, therefor the younger one may be feeling a little left out using rages as a way to get attention from mom. Mom needs to get a handle on the depression with use of meds (imo) and try to set time out specifically for the one throwing rages. In the mean time she needs to let him know she loves him and cares about it. A six year old isn't very well equipped to deal with adult emotions (stress, anxiety, anger, ect). Hopefully no one is badmouthing the other parent when the kids are present, this to can have an impact on the childs behavior. My ex used to bad mouth me all the time and lets just say I have had my hands full. (actually been kind of a nightmare) but awwww well life is just a movie right?
Maybe when the 6 yr old comes back home you can ask him how his visit went at moms and see if you can pinpoint a particular behavoir that is happening. (the impulsivity of the adhd child pulling 6 yr old strings)
Hard to truly say. I do know from experience about those I mentioned. (and still learning)

Burned out mom
Peg
good luck