“does a bankruptcy filing affect my ability to sponsor my family to come to the U.S.?”
No, a bankruptcy filing, under either Chapter 7 or Chapter 13, does not prevent you from sponsoring family for immigration benefits.
When you sponsor a family member, you need to file an I-864 Affidavit of Support. With the I-864 the Government wants to make sure that you earn a decent income (125% of the Federal Poverty Guidelines), and it determines this by looking at your Adjusted Gross Income (“AGI”) from your recent tax returns.
So the I-864 cares about your gross income, not about how much you spend and your debts. Filing bankruptcy does not affect your gross income, so filing bankruptcy does not change what you report on the I-864. Filing bankruptcy helps to *reduce* your debts and therefore actually increases your net income, which is a positive thing!