What is the ruling on a woman who, upon entering ihram to make up a previous 'umrah, said: "Here I am, Allah, for 'Umrah, I intend to make up the 'umrah," after her 'umrah was invalidated due to menstruation and intercourse occurred before she could make it up, and she does not possess the money to slaughter the sheep required of her?

Menstruation does not invalidate 'Umrah (definition), but it prevents circumambulation (Tawaf (definition)). If you left Makkah without performing Tawaf and Sa'i, you are still in the state of ihram (definition). You must return to perform Tawaf and Sa'i, then exit the state of ihram. It is not prescribed to enter ihram again. If sexual intercourse occurred before exiting ihram due to ignorance, the 'Umrah is not invalidated according to many scholars. You would be required to offer a sheep (shah) if you consented to the intercourse; otherwise, your husband would be responsible. Regarding other prohibitions of ihram: for those that involve destruction (like cutting hair and trimming nails), a single fidyah (definition) (expiation) is required for each category. For those that involve luxury (like wearing tailored clothes and using perfume), there is no penalty if it was done out of ignorance.