Wow! I thought it was just me! I learnt flute as a kid. To play flute you only need to learn the treble clef notes. I can read those fluently but not so much the base.

I suggest you find some time to play the base clef game. It should help cement the knowledge you are acquiring.
I felt quite confused often playing the games as I went from treble to base and back. It takes a bit of practice but you will get it. If I don't play them for a while I can still get mixed up. But this doesn't bother me when I am playing gentle piano. My hands have no trouble remembering that they get one staff each! So in the end it doesn't matter to your playing, just you ability to name ( and thus sing) the notes. When we are learning to play songs we only sing the melody of the treble notes so it doesn't hurt to be more confident in those in the end!

once again it is a case of just believing it will all sort itself out in the end. You may not realize just how often you are drawing on those skills you already have as you learn these new techniques. I had no idea until some others posted comments on my progress diary asking how I did that.
Helene recommends people start with the game Guess Key. Playing it daily ( or often at least) for the first month, for a set time and record your score each time. So the progress you make is clear and motivating.