All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The ruling in this case is based on knowing the intention of your friend behind inviting you and your family to dinner. If you cannot be sure of her intention, you may act according to what you predominantly think about that. So, if you predominantly think that the reason behind such invitation is to delay repaying the debt and not ask that woman for repayment, then you should not accept her invitation, otherwise there will be no harm in accepting her invitation. That is because scholars have stated that if the gift of the debtor is not due to the loan, but because of family ties or friendship or a usual habit of giving gifts before the loan was made, then there is nothing wrong with accepting the gift in that case.
Allaah Knows best.