If I was awarded a business in my divorce, and file bankruptcy because I was not able to refinance, what happens then?

It is impossible for me to speculate when I know only the small bit of information you have provided. The party that is likely to take your business and sell it is most likely going to be the bankruptcy trustee assigned to manage your case. The sale proceeds would be used to pay your debts. Your ex spouse could sue you for failing to comply with a property and debt division of a bankruptcy unless your case is handled by an expert in bankruptcy and family law. Which is why you need an attorney with top expertise and experience. Proceed with caution or you will shoot yourself in the foot.

There are too many variables to hazard a guess. Meet with an experienced bankruptcy lawyer and pay them for one hour of their time (between $250 and $300). Save your self a lot of grief!

This sounds like a potentially complicated situation, so you should consult with a lawyer who has experience in bankruptcy and domestic relations. In a typical chapter 7, a business would be liquidated by the trustee. If the trustee would get the best deal by selling the business back to your ex, s/he would consider that. Whether your ex could "come after you" would depend on the terms of the divorce decree.

Without seeing the divorce decree or the paperwork on the transfer of the business, I can't give you the answer in this case. However, generally, your ex would have no right to take the business back nor would he be able to come after you.

I'm afraid that doing right by your three kids is not relevant to the decision-making of a bankruptcy trustee or Judge. The question will be what is the value of the business (and there are several ways of appraising a business), and can you exempt it under the (federal) laws of bankruptcy, or under your state law, if it is applicable. I doubt that your ex-husband has any special rights to the business under the facts you stated. I strongly recommend you retain a skilled bankruptcy lawyer to advise and represent you. Your situation is a bit more complicated than the most basic chapter 7 cases, and the assistance of such a lawyer is likely to be well worth the investment. Good Luck.