One of the basic premises of PGP encryption is that you receive a key from someone you know is a valid entity, then you verify that key by signing it and setting trust. That ensures that a key is not automatically trusted, which is a security precaution.
The party you sent the key to is responsible for verifying the key to make sure it came from a valid source (confirm that it is your key by checking the fingerprint with you, etc.), and then trusting that key appropriately. Internal keys are verified because the internal users will see that their organization's keyserver issued and signed the keys.
There is no method for having a key automatically be trusted by an external user. This is by design. There is no need to sign your organization key.