What is the ruling on the umrah of one who left the circumambulation (tawaf) to search for her family, then completed the umrah with them, without knowing how many rounds she had performed, and does she remain in her state of ihram, and what must she do now?

You erred by not completing the 'Umrah and performing it in an insufficient manner, and you are still in a state of ihram. You are obliged to go to Makkah to complete the tawaf, sa'i, and taqsir (shortening of hair) to exit the state of ihram.

You must refrain from the prohibitions of ihram after becoming aware of them. What you did out of ignorance carries no penalty, but it is more cautious to offer fidyah for destructive prohibitions (such as cutting hair and trimming nails), which is: fasting for three days, or feeding six needy people, or sacrificing a sheep.

If you are unable to go to Makkah and complete the 'Umrah, then exit the state of ihram like one who is prevented, by sacrificing a hady (sacrificial animal). If you are unable to do so, then fast for ten days, by analogy with one unable to offer the dam al-tamattu' (blood of enjoyment), then shorten your hair, and by that, you will exit your state of ihram.