Is the aforementioned Umrah valid, along with its accompanying renewal of the intention of Ihram by saying: "And if a barrier prevents me, then my place of release is where You have prevented me"?

The validity of the circumambulation (Tawaf) depends on ritual purity from menstruation. If you have performed the ritual bath (ghusl) after confirming purity (either by dryness or the white discharge), then any yellowish or brownish discharge after the ghusl does not matter if it is outside your usual period, according to Umm Atiyyah's statement: "We did not consider the brownish and yellowish discharge after purity to be anything." However, if you have not confirmed purity, you are still menstruating, and the Tawaf is not valid according to the majority of scholars. You are required to return to Makkah to complete the 'Umrah while still in your initial state of Ihram. If you are unable to return, you may exit the state of Ihram like one who is prevented. If you had stipulated at the time of Ihram that you would exit it wherever you are prevented, then you may exit it without penalty.