It sounds to me like Rob really doesn't want to spend time with you or your DH but just doesn't want to come out and say it. I will say having been in a position where there was pressure to visit my father even though I didn't want to it is a really hard place to be. I put on a good show while I was visiting, but I did try to avoid it. It was miserable for me. OP, from what you have updated, it seams that Rob and Michelle are closer to his mom and Step-dad. Even though in my head I understand that the mature thing to do would be to tell your father you didn't really want to spend time with him, that is much easier said than done. I can't tell you the amount of judgement people get when they dare express that they don't want to spend time with a parent.
I'm not saying that you DH had done anything wrong, but there may be some discomfort on Rob's side that he doesn't know how to express or feels that he will be attacked for his perception.
How long has it been since his parent's divorce? Who did he live with? Is he the oldest? Just because his brothers were able to shift their actions doesn't mean that Rob feels the same way they do, He may be too lazy to commit or might have other feelings that are in the way.
I believe Rob was 19 or so when DH and his ex split up. He was in college at the time, so he was living on campus in OurCity. Shawn and Joe stayed with their mother in the family home. DH moved out to a small apartment. He didn't have room in the apartment for the boys to stay. A tremendous point of sadness for DH is that even though they all lived in OurCity, he wasn't as able to spend time with them as he had been before the divorce. There were multiple reasons for this, but the main one was the stipulations in the divorce decree. He was required in the decree to maintain the mortgage payments on the house, pay child support, and pay 2/3 of the college expenses for all three boys. Very quickly it was obvious that he couldn't keep up financially, and he had to get more jobs to meet those obligations. When I met him 7 years ago, he was working four jobs. A small apartment and a very old car were the best he could do for himself. He was paying car insurance, college, car payments, mortgage, monthly child support, and all sorts of other costs to support the boys. I have never seen anyone as overextended as DH was. The boys have gotten older and finished college, so those expenses have now dropped off. DH (and I) have a more comfortable lifestyle than we did when we first were together.
Joe had the hardest emotional hit at the time of the divorce. He also is the most aware of what DH was sacrificing in order to meet the financial obligations in the divorce decree because he saw more of it firsthand than Rob and Shawn. Still, I'm not sure whether Joe completely understands how much DH had to do put him through college. Shawn has come to see why DH did what he did at that time. There don't seem to be hard feelings toward DH, but I do think Shawn has some residual "stuff" from observing his parents' relationship
when they were together. Rob is the tougher nut. Before DH and I were married, he would give DH a very hard time about driving those "old beater" cars and living in small, crummy apartments. I heard him question DH about it on many occasions. DH gave evasive responses because he didn't want any of the boys to feel bad about the sacrifices he was making to support them, and he didn't want to badmouth their mother. Where we used to have more frequent visits with Rob where he would pick at DH, we now have fewer visits with Rob and less picking.
Ellebelle, to answer your most recent post, to my knowledge DH and Rob's relationship
was mostly positive before the divorce. DH was the model dad: soccer coach, heavily involved, and highly participatory. I am aware of only one significant issue between them when Rob was a teenager, but that was way before the divorce and it also involved Rob's mother. As I say above, the participatory nature of DH's relationship
with the boys changed mostly for Shawn and Joe after the divorce because they were still at home. Rob wasn't, so that end of things wouldn't have affected him directly. DH has wondered off and on if Rob believes DH abandoned his mother, but he isn't sure. That isn't what happened though.
I just remembered this ... After DH had his heart-to-heart with the boys a few years ago, we noticed that Rob started doing some PA things. For example, let's say we were supposed to meet the boys for lunch somewhere. If we weren't at the restaurant first, Rob would start texting DH to ask where we were. The answer was as simple as we were parking the car and would be in the restaurant in two minutes. Even after DH replied to Rob's text, Rob would keep texting. It happened over enough get-togethers that it was an annoyance. It felt like an attempt on Rob's part to try to make a point that we were holding him up. DH never said anything to Rob about it, and it stopped after Rob and Michelle started seeing each other.