First, thanks to everyone for their responses in this thread. I appreciate the suggestions and insights.
DH and I had a long talk about this situation last night. He told me he was awake in the middle of the night Sunday night thinking about it and wondering how he got himself back into the situation of waiting around for Rob that way. I told him that if it were any other day (not Father's Day), I probably would have pushed him harder to let Rob off the hook so to speak and move on with our day without him. We agreed that we both were holding out hope that maybe Rob would come through this time with a more substantial visit because it was Father's Day. DH is feeling let down about Rob's behavior in general, but especially because it happened on Father's Day.
I made a comparison between Rob and my mother and brother, whom I have posted about several times on eHell. The two of them have a pattern of making plans together and not informing me of them until the last minute. Where in the past I would drop everything to try to make it, I stopped doing that several years ago because it was crazy-making and I was becoming resentful. I asked DH last night what we would have done if it had been my mother or brother behaving the way Rob did on Sunday. He smiled, and he said, "We would have said no." And he's right, that's what we would have done. So the question was, "Why is it different with Rob?" DH said, "It shouldn't be different with Rob."
I also shared Hmmmmm's point, which was hard to talk about, but necessary. If the tables were turned, and if DH were the adult child and Rob were the parent, would we accept Rob's behavior? Would it be okay for Rob as the parent to snark at DH in the way he does? Of course it wouldn't be.
We have agreed on the following:
1) We need to do a better job of initiating plans with Rob and Michelle. We must loop Michelle into the planning so it doesn't just fall off the radar like it does when only Rob is involved. How that plays out, I think, will tell us a lot about Rob's real feelings/intentions. If we loop Michelle in and it still doesn't work, then I think we're dealing with a deeper problem.
2) When Rob tries to pull one of his last-minute "drive by" visits, we need to give more thought to our initial response than an immediate "yes" to a text of "Will you be around this afternoon?" DH realizes now that the immediate "yes" is what's putting us on the hook. I gave DH the suggestions from PPs about calling Rob back to talk specifics rather than replying to his texts so we have a better chance of pinning him down. If Rob refuses to answer the phone and doesn't respond to a message, then our response needs to be, "Looks like it won't work out this time. Maybe next time."
3) If we agree with Rob on a time to get together, and he doesn't show (or if it's getting so late that waiting for Rob is bumping up against our plans), we can use the same line as above: "Looks like it isn't going to work out this time. Maybe next time."
DH and I talked about how a change in his behavior might affect Rob. DH will have to be prepared for the possibility that he may see Rob even less because Rob may not respond well to a change in DH. DH said he understands that may happen. At the same time, if we're countering it with initiating more invitations on our end, we can hope that it may balance out.
DH was glad we talked about it. It seems like it was really eating at him just as it was eating at me. Thanks again for the replies and suggestions.