Regarding gift tax, you are correct in that no gift tax will be owed. For 2016, gift tax does not apply unless gifts exceed $5.45 million. No tax will be owed; however, your mother-in-law will need to file a gift tax return (Form 706) because her gifts to both your wife and her brother exceed $14,000.
As the co-op was sold after your wife and brother-in-law took ownership, they are responsible for the capital gains taxes. Because it was owned long-term by your wife and brother-in-law, the preferential long-term capital gains rates apply. At the income level you describe would be no more than 15%.
Also keep in mind that for gifts, you use the donor's basis as your own cost basis for calculating the gain. So if, for example, your mother-in-law had cost basis of $50,000 in the co-op, the total gain would be $200,000 ($250,000-$50,000).
Your wife and brother-in-law would each pay tax on half the gain, assuming 50/50 ownership. Your mother-in-law does not owe any taxes on the sale because she does own the property.
Please let me know if you have any follow-up questions or need clarification. If this fully answers your question, please rate the answer to close out your inquiry. Thank you and have a wonderful day.