What you describe as your wifi in being controlled let fear a Man In The Middle attack. The encryption of Whatsapp message is more than enough to be protected from that. Someone just eavesdropping what is exchange over the Wifi network will only see encrypted messages and will not have access to the actual content.
Now if your question does using Whatsapp guarantee that nobody else but the recipient will ever see the messages, the answer is quite different. The protocol used by Whatsapp is indeed secure, but it looks like the implementation willingy choosed ease of use over security. It has been discussed at Whatsapp security, and a comment gave a link to the Guardian explaining that
A security vulnerability that can be used to allow Facebook and others to intercept and read encrypted messages has been found within its WhatsApp messaging service
However, WhatsApp has the ability to force the generation of new encryption keys for offline users, unbeknown to the sender and recipient of the messages, and to make the sender re-encrypt messages with new keys and send them again for any messages that have not been marked as delivered.
The recipient is not made aware of this change in encryption, while the sender is only notified if they have opted-in to encryption warnings in settings, and only after the messages have been re-sent. This re-encryption and rebroadcasting of previously undelivered messages effectively allows WhatsApp to intercept and read some users’ messages.
[Whatsapp justifies that to cope when] a contact’s security code has changed. We know the most common reasons this happens are because someone has switched phones or reinstalled WhatsApp. This is because in many parts of the world, people frequently change devices and Sim cards. In these situations, we want to make sure people’s messages are delivered, not lost in transit.
So Whatsapp main design is useability and not security. Full stop. For most usages it is fine, but if you really need a high Confidentiality level, choose a tool dedicated to security like PGP or S/MIME encrypted mail. Not as sexy but far more secure.