I ignored the Doctors advice and Mom is doing very well. How do I deal with family that thinks I'm still wrong?

I don't know how your family can think you're wrong. The proof is in the pudding, yes? Maybe without realizing it, you were making her feel as if you thought she'd done something wrong...should have been doing things differently...made mistakes with mom's care...you get the picture.

IMO, there's bruised ego involved. Not your SIL thinking you're actually wrong. You may be a very straightforward communicator who didn't give a second thought about how your report of talking to the doctor may have sent the message that she dropped the ball.

It may even be the way you FEEL. Orrrr, you could be so proud of yourself that you're doing a bit too much crowing. ;) (BTW, I'd be darned proud.)

At any rate, SOMETHING ruffled feathers. Figure it out and fix it would be my heartfelt advice.

On another note, even lame atempts by family could be encouraged and fostered into a real relationship. If we take a hard look at ourselves and consider how long if took to become good at caregiving, and that we need relief and help to continue, (it's alled respite care), we may be able to tolerate a sibling willing to drive the patient to the doctor's.
Of course, only you know the sibling, and many here have siblings to ignore for the sake of ourselves and our parents. Trust your own instincts and experiences.
Do you really have to report to SIL or brother what you did and did not do as far as doctor's advice? I report everything to my own detriment at times, wanting to share is normal. Since I am doing what is right, I could keep it to myself.
You can post here, like you did Jackboy. This is your post, if you just want to vent, that is okay too. I am used to having discussions by myself, but there are so many who can relate to you.

Family too, should be ignored.

They are something, aren't they? These family members that do not do one bit of the care and want to attend the doctor appointments. Happened here too, though I went and sat there quietly while doctor asked questions. Naturally, the conversation returned to me as sis had no idea how to answer. Kind of funny, the sudden concern and not a clue what to talk about or how to answer. The end of these appointments were alway wonderful as the doc would give me these inquisitive looks. Doc was puzzled and what cauaed this? Dysfunction, naturally.

Yes the one who does the lion's share of the care giving usually knows best. Doctors don't always. They have their patient's best interests in mind but they aren't in the trenches day in and day out.

Yeah, whine and vent. It is a lousy setup.

Maybe SIL was looking for a way out of taking Mom to appointments and to make it look like your fault. Maybe it is about control or pride.

Whatever it is, you don't have time for it.