If I had to guess at a motive right now I would say it was a combination of some sort of attempt at revenge against the mother (if the 2 were actually involved with each other prior to crime) and robbery. I know there have been a lot of comments about how this area is a "drug den," etc, but in my opinion, its not much different from any other poor, rural area in the South. In these areas you can always find a very booming drug market if you look hard enough or know where to look....sometimes you don't even have to look very hard. Also, not unlike many other areas in ALL parts of this country, there are some very evil people who live among everyone else and these people don't have a conscience or care who they hurt as long as it gets them whatever it is they are after.....whether that be money, drugs, revenge, etc. On top of all of this, you have just your "regular" criminals who basically make a living off of stealing cars, breaking into homes, etc and all of these individuals are usually somehow intertwined (either directly or indirectly) in an area like this. Living among these "bad" guys, are people like Mr. G who have nice houses and appear to be "rich" to a majority of the community, even though these people may simply be middle class and not "rich" at all. Obviously, these "rich" folks stand out and can easily be targeted for crimes.
In my opinion, the suspect (and possibly others or at the prompting of others) set out to rob Mr. G and he probably knew that he was babysitting the twins on that day. He knew that Mr. G would probably be at his most vulnerable with the kids present and be as compliant as possible hoping that no harm would come to the kids or himself if he cooperated. Not only do I think the suspect probably believed or actually knew Mr. G kept money and other valuables at his home, but I think the car may have actually been a target too. There is a booming black market for any type of auto parts, especially those from imports such as an older Benz since certain items are difficult to find for these cars and when you can find them they are expensive. I think it could have been as "simple" as someone the suspect knew saw Mr. G's car and knew someone who needed/wanted certain parts from that model car, even if it was just the doors. Although, I have a feeling that if the doors were the only things that were actually removed from the car then whoever was doing the "chopping" was interrupted before they could finish getting everything they wanted since there are other valuable parts on that car that could easily be sold. Also, it doesn't make sense that the only evidence of the crime was on the 4 car doors, front and back, but no other part of the car and the doors were removed to try and conceal evidence. If there were bullet holes in the doors, there was blood all over the doors and everything else in the interior of the car, so simply taking off the doors would be a time-consuming task that accomplished nothing to help hide evidence and actually would have created another problem since the doors would then have to be disposed of in some manner in order to conceal them. If the car had evidence in it that the suspect wanted to destroy then he would have set the car on fire or drove it into a lake/river. Also, based on the limited reports we've seen, it appears the victims were probably killed where they were found based on the amount of blood that's been reported as being present on the dirt road.
I think the murders may or may not have been planned by the suspect prior to the robbery attempt and we may never truly know the answer to that, but no matter what, there were 3 innocent individuals murdered in cold blood at the end of the day. It doesn't really make sense to me that the suspect would have the intention of murdering all 3 during the course of a robbery since there would have been (I assume) plenty of better opportunities for him to murder Mr. G or the kids if he truly wanted one or all of them dead for whatever reason. If he wanted revenge on the mother and thought he could get that by murdering her children, he could have hurt her a lot more by actually murdering them in her presence and it would have presented a much less risky situation in which to do such an act, rather than doing it when the kids are with a grown man who could potentially defend himself and the children against such an attack, at least better than the mother could most likely. I think the suspect probably arrived at Mr. G's home to rob him and something didn't go as he planned, whether it be that he allowed them to see his face or they recognized his voice (if he was attempting to conceal his identity since he just planned on stealing from Mr. G). This curveball probably led to the suspect thinking he had no other option other than to eliminate the witnesses, which he may not have minded doing anyway, especially if he was angry at the mother for breaking up with him or for some other reason.