How can one balance spending on a large family with repaying numerous debts, especially if the income is small and insufficient to repay any of the debts?

The maintenance of those whose upkeep is obligatory takes precedence over repaying debt. One should begin with maintenance, without extravagance or stinginess. Whatever remains thereafter should be spent on repaying the debt. What is obligatory in repaying debt is to exert one's utmost effort and ability. And whoever borrows with the intention of repaying, and does not neglect to do so when able, then there is no blame upon him if he becomes unable or delays, due to the Prophet, peace and blessings be upon him, saying: "Whoever takes people's money with the intention of repaying it, Allah will repay it on his behalf; and whoever takes it with the intention of destroying it, Allah will destroy him."