Getting a 1099-S has nothing to do with whether or not you need to report the income. You need to report all income unless there is a exception.
If the house was in your mother's name (or her revocable living trust) when she passed, then whoever inherits it gets a step-up in basis to it's fair-market value as of the date of her death. Not the date probate was finished or the deed was prepared or filed. The realtor's analysis will probably be ok, but could be challenged. A licensed real estate appraiser would give you much stronger support for your basis number, but would cost more. Probably won't be an issue for this $ level and an obvious break-even or loss situation.
Each of you would report your % of each item (proceeds, cost of sale, etc.)
As @Hal_Al mentioned if the property wasn't rented you might be able to claim a loss. Whether you can actually do that is a surprisingly complicated legal question that really requires a tax-attorney familiar with your facts to answer. In prior years I had answers that detailed why that was the case, but in this new system I can't find that easily. I think you probably can, but it isn't black and white.
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