Is congregational prayer considered valid if performed after its prescribed time due to uncontrollable work circumstances, and if it is performed with only one other person?

If you vowed to pray in congregation at the mosque, then your prayer with a congregation outside the mosque is not considered fulfillment of the vow. And vowing to maintain congregational prayer in the mosque is a vow to perform something that is already obligatory by original Shariah law, and this vow is not valid according to the majority of scholars.

However, if you vowed to pray in congregation absolutely "under any circumstances," this is a vow to do something that is not obligatory upon you by Shariah and that you cannot fulfill, and its expiation is like the expiation for breaking an oath.

If you intended absolute congregational prayer, then the minimum congregation is two: an Imam and a follower. So if you pray with an adult, you have fulfilled your vow.