Wow. That's awful, livinglife. I empathize completely. This would be a much easier situation if 1. your brother didn't have issues, and 2. the two of you didn't have an uncomfortable history (i.e. not the best relationship).
I have an idea as to what you might do, which could be good (because I'm also an ESTJ and therefore have a semblance of insight) or bad (because I'm not the best at solving interpersonal issues...).
I can tell you right away that he made those stupid criticisms of your care for your mom because he desperately wanted control of the situation. He was convinced that he could do better at the job than you (for whatever reason). But to answer the OP... I'm inclined to say yes, or at least maybe. But one question must be answered in order to salvage the relationship between you two: "What's his PROBLEM?"
As an ESTJ, I know that we are very blunt people. We generally don't like to lie, or beat around the bush, or sugarcoat information to make people feel better. Generally, if you ask an ESTJ a question, they will answer it truthfully (and if they try to lie, they'll most likely suck at it). So (and this might be an absolutely terrible idea - you know your brother better than I do): ask him what he thinks of you and why, or something to that extent that's phrased better, and with something leading up to it. If he's like me, he will answer the question fully and truthfully (that is, if he even wants to communicate with you, and if he doesn't, my idea is pointless). From there, you guys can figure out what's been going on historically with your relationship, possibly debate a little, have a good cry, and come to a mutual understanding.
p.s. on the whole type relationship argument, I side with evan. Those relationships look good on paper, but there are loads of other factors to take into account.
EDIT: In response to Hmm, your brother probably either 1. doesn't think he's done anything wrong and therefore won't apologize, or 2. is embarrassed and/or full of pride and... therefore won't apologize. If you speak to him bluntly, logically and matter-of-factly about it, you might be able to get that answer from him. ESTJs and INTPs work great together when they're having logical conversations about FACTS (and I know because I have an INTP dad, and some of our most fun and lively conversations have been about magazine articles and scientific studies and such).
ANOTHER EDIT: Sorry about this, but I just reread the OP and how, to your father, your brother was always wrong and you were never wrong. (I missed that part...

) He's probably trying to get back at you for being miss perfect... maybe he's trying to prove himself as well?