Where did the "play on realms" option go?
To have the Play on Realms button, you must have a server or be invited to a Realms server.
If you are invited to Realms, you would have a main menu looking like this:
If you are not invited to Realms, you would have a main menu looking like this:
If you want to connect to an external server, tap Play and then Edit. Tap external and then press add. Tap on the server and you should be able to connect. Using the Minecraft for Multiplayer App should be similar.