I totally disagree.
You don't know for certain that a divorce is imminent. That may be wishful thinking on your part. Only they know for sure what is happening in their relationship. I would, personally, stay well out of it. It's not anyone else's affair. But you certainly should discuss other family matters, such as your parents' will, with him.
I think it is untrue to say that a family member will remain as important to a sibling as their spouse. I think actually that the reverse is true and that the pattern of switched allegiances is perfectly normal. My husband is more important to me that any family member. That's how it should be. He is my life. He is the one who knows me best, with whom I share incredible intimacy. No other family member can know us or be quite as close to us as a spouse.
Personally, I think she may have something here. I have, in the past, spoken to my brother in law and said the same thing to him as your SIL says to you: please do not discuss certain matters with him, he is under enough presure right now. The reason? The spouse knows better than a sister or brother exactly what pressures the other spouse is under. She knows him better than you do: bottom line. Maybe she really is trying to help him, protect him in some way.
I think you need to control your anger toward her. Dissipate it somewhere else. Don't participate in their spousal problems: that's what your SIL is really trying to tell you. I would do the same if my husband's family wanted to interefere in my relationship with him, however bad it got.
If your brother seeks your input, that's something else, and that's up to him. Ideally, wives do not "just come and go" as you mistakenly think. To believe your SIL to be so negligible is not respectful at all. I don't think it does your brother a great service either: what does it say about his character?
Calm down: take a step back from someone else's affairs, then address with your brother the affairs that have to do with your joint parents. The rest I would leave well alone.
You may not like what I have to say here. I have been honest and you have the right to ignore it as you wish. But, there are always different sides to a problem, and sometimes it can hurt to be forced to entertain another perspective. But also, it can be productive.
I wish you well, and above all, I hope your brother can sort out his marital problems successfully.
Clare