I've noticed a big reason I have trouble with some chords is that the first joint near my fingertips cannot bend much when my fingers are somewhat straight. When playing a Dm7 barre chord with the root on the A string, I can't get my finger on an angle enough to stop the D string from buzzing. Can I manually use my other hand to start stretching this by pulling it down while not playing?
As already said, this is not a particular problem of yours. People in general cannot do this either, but good new is: it's not necessary in order to play the chords properly.
The only way out is practice. Barre chords are a hard thing to learn, I guess everybody has once struggled with them, but with time you will find a way to play them easily.
And I don't think pulling you finger while not playing will help, nor is healthy.
Nobody's first finger joint bends much independently of the rest. Yes, if the human hand was constructed differently, guitar playing might be a bit easier!
I think you are asking about A form barre chords and finger 3 - ring finger - playing the fifth of the chord...
Fingers: 13141 Fretting: x57575
When I initially bend my fingers to play the chord my finger 3 seems to bend about 20 degrees at the first join. It doesn't really bend more unless I roll up my whole finger which would put the finger way out of position for the chord.
After my fingers first contact the strings and the fingers are secure that first join bends some more, but it's from sort of pushing into it. It bends maybe to 30 degrees.
It seems to me I'm bending more at the second join.
I'm not really suggesting measuring degrees, but I'm trying to give some basic idea that it isn't much more of a bend than letting your fingers relax into a neutral curled position. Meaning when your hand is relaxed your fingers curl up partly.
From that relaxed position most of the bend seems to be at the second joint.
Also, keep in mind this A form barre chord is derived from the open A chord. You might try playing it without the barre down at the 2nd fret. If you can play it cleanly there, it should be only a matter of sliding up to higher frets and then placing the barre with your 1st finger.
I broke my pinky finger at the first joint, never got it fixed as I thought it was a sprain, and now the top of my pinky doesn't bend over - by itself. (It's actually called Swan Syndrome.)
So what I did was bend the finger (make a fist) and put tape on the joint, like the size of half a stick of gum, masking tape, whatever, and put it in a position where you don't need much more effort to get it to bend more.
If you want something to take along try cut down nasal strips.