@gingin is the plant an Epidendrum (orchid) or an Epiphyllum (epicactus) just for clarity.
The wrens might be nesting in it repeatedly because it affords good protection from cats and raccoons (if it is a cactus, it has thorns). But I'll bet you don't want to move it since it's probably big, and leggy and prickly.
Being a cactus or an orchid, it probably won't mind if you only water parts of it - they feed and get water through the stems as well as from the roots. So if you can get by with just spraying the stems until the wrens are finished their nesting operation, that would be the best thing.
