Presuming that the two channels aren't associated with the same account directly (e.g. available in the https://developers.google.com/youtube/v3/docs/channels/list) - worth a check if you haven't.
If they aren't (which is what I suspect), then this is a bit tricky. The way multiple accounts are handled is via associating a Google+ page with the YouTube username (so a given Google account can have several pages/youtube usernames associated). I suspect your first one is associated page, and the second is attached to your main Google profile. This is in part to keep them separated - so no one has to know you're both unless you want them to.
On the web, the user will get a chooser for which account they want to use, but unfortunately this isn't supported on Android at the moment. The only way to log in as that user in Android is to create a password for the page associated with the YouTube channel you want to use, and adding that in the Android account manager: https://support.google.com/plus/answer/2882201?hl=en-GB