Trouble with bar chords. Cant hit all strings

I don't know if its something I need to "get used to" or if its a problem I won't be able to overcome. Ive played guitar for 13 years and haven't noticed this until now that I'm taking classical lessons. My teacher showed me an exercise where I have to use bar chords and I have trouble getting all the strings to sound.

Basically my problem is that my finger that I use to bar doesn't push all the way down on the 3rd string (G). All the other ones are fine, but the G string lies right on the part of my finger that is in between the joins, so it doesn't press down as far (if that makes any sense). All I get is a muted sound. When playing arpeggios its noticeable because one string is just dead. If I push down harder it works better, but I have to really push down hard to the point that it will be painful to play long like that using that much pressure.

Anyone else have this problem or have any recommendations?

Isolate your problem. Look at what part should touch the string, and correct that. For now don't worry about the other finger's, just the one needing attention. Then strum slowly and listen if all the strings sound out like they should. If not, keep correcting the problem. Once you fixed that problem, than add your fingers to the chord. But make sure that you used the same new method as you were before.

Ive tried that, but the position that I have to be in to play doesn't give me the reach I need to add more fingers. I can bar with one finger just fine, but when I do a chord (specifically a C chord that I have to bar at the 8th fret for example) I can't get my pinkie up where I need it to without slightly shifting my first finger, which mutes the string again.

It should take only a small adjustment of your finger up or down to get the string onto a fleshy part instead of the joint. If that doesn't work try rolling your finger just a bit the side, less flesh more bone.

You'll get it.

I prefer a slightly different approach to solving the finger joint problem, as I used to suffer with it myself. I simply "move" my finger joint onto a string that lines up with a covering finger - for example on an Am7, 575555, I would have the joint of my finger on the A string, this way it rings true due to the finger covering it.