This is a truly tragic for all concerned, you all have my deepest sympathy.
I've given this a little thought since you first posted this thread.
I have come to the concussion that there is only one course of action that could not lead to any future strife.
If I were you I would freeze the "Business", "Company", "Partnership", I'm not sure that what you and your bother had conforms to any of these, but you SIL does, so to avoid upset I'd just accept her definition. I would then suggest you sell the whole thing, "as is", "lock,stock and barrel" and then split the proceeds. In this way you are putting yourself and your SIL very much "in the same boat" so to speak.
This way there is no scope, now or in the future, for you SIL to feel short changed.
Your business was YOU and your BOTHER, it was you two who bought in the work and you two who did the work and thus generated the income, unfortunately your bother revenue generating ability died with him. It appears your SIL thinks the business generates its own revenue, to which she is entitled, unfortunately small tree firms don't really work like that, sure being established make finding the work a little easier, but the work still has to be done in order to turn any enquiry into profit.
Trying to convince your SIL that the business has very little value and that it does not throw off any passive income could be very difficult. The easiest way to find any items true value is to sell it.
Obviously I don't know your circumstances and you may not be able to do as I suggest, but IMHO it would be the best long term solution. At least this way you and her are both in the same position, there is no scope for any future claim on yourself.
Could you just sub out for now and then start up again in the future?
Business with family is notoriously difficult, the relationship with you bother must have been very special and must make your loss all the worse, I really hope you can resolve this situation in the least painful manor for all concerned.