Try a 'join' instead of a 'relate', which will add the table columns to your point dataset and then you can filter based on them.

ESRIs help on the topic:
http://desktop.arcgis.com/en/arcmap/10.3/manage-data/relationships/deciding-between-relationship-classes-joins-and-re.htm

Here's a similar issue:
https://gis.stackexchange.com/questions/175154/querying-through-relations?rq=1