I'm sorry partiallysunny. This is so tough, and must be really disappointing.
I think there are a couple of things going on here. Like you, I need to be invited to someone's house. That goes for anyone. Then add to that the health issues your mom and dad have, and I definitely agree that your priority in this is your DS. You need to know that your dad is stable before you go there so that your son doesn't see anything he's not ready for or won't understand. Maybe that's something you can reevaluate as he gets older, but for right now, it is what it is and this is the approach you need to take if you're bringing him with you to their place.
I also really think that your brother has to be out of the equation when it comes to your relationship with your parents. Don't get me wrong, I think you've handled your talks with him about this really well, but I wonder if the better thing to do (for your own sanity) is to just not engage him at all when he tries to lecture you about your mom and dad or speak on their behalf.
I mean, I don't know your family, but think about it this way: if you started contacting him to give him grief about his relationship with your parents, would that be okay? Maybe it would, but my guess is the answer to that would be a resounding no. Well it's not okay for him to do either. Your relationship with your parents, whatever you want it to be or want it to look like, is just that - yours. Period. I would just stop talking to him about it, because I think he treats that as you justifying things or explaining yourself, when you don't have to. This is all between you and your mom and dad.
Say fuck it all, if you need to. Even temporarily, if you just need a break for a while. Or, before saying 'fuck it', you can try to approach any visits a bit differently. Leave the ball in their court. When your mom expresses interest in seeing you, plan a day and time to come to her place. Before you leave, call her to make sure you're still okay to come over. If it's not a good time, if dad's having a bad day, fine. You tell them that's okay, and that you love them and hope they have a good day. Done, and done. You tried, and you still get your weekend and your time with your own little family. I realize this puts more of the onus on you to check with them, but it also means that the idea of a visit was theirs. Let them come to you, and stop pursuing them for a while, because it's only hurting you. It's up to you, hon. I don't know if that would work or not, but it's something to try.
I have pointed out to my brother that he needs to stay out of things between my parents and I, even before he put himself in the middle of that last one.
Of course, he acts all innocent and "what am I suppose to do?" Of course he doesn't know how to say "you need to talk to PS if you have an issue with her" and drop it. No, my brother is a fucking busy body and likes to be in the middle of the "action".
I don't usually engage, but I was extremely tired at the time and my emotions were running high. Usually, I would start with "mom has my number and knows how to call me if she has something she wants to talk to me about", but the bash on the ILs and all the "it's not fair" shit got to me and I felt the need to not only defend myself, but my ILs and to point out their own hypocrisy.
Lower your expectations and give them a deadline to be at your home. If they are not there by a certain time then go about your business. Your brother loves being the golden child and he is actually doing more harm than good. Going through a middle man is just adding a step which keeps you and your parents from direct conversations. Cut him out and you might find he is also causing you stress. I find when one of my sisters disappoint me I remind myself that is who they are and not who I dream. Sometimes they're simply incapable of being polite or acting in an acceptable fashion.