BTW, I play the chords as follows (the number representing my finger instead of fret for illustration purposes)
G:
_4__________
____________
____________
____________
_2__________
_1__________
Everyone has their own opinion when it comes to chord shapes. You play the same form as I do with C and D Chords. The G chord is different from mine or maybe it's numbered incorrectly. Try your G chord using this fingering shape and see if it helps.
G:
_3________
__________
__________
__________
_1________
_2________
Using this shape emphasizes the third note (a Major chord is basically determined by the 1st note (Root), third note and fifth note). In this case the Root note is "G" (2nd finger, 6th string, open 3rd string and ring finger 1st string), the third is "B" (1st finger 5th string and open 2nd string) and the fifth is "D" (open 4th string).
When making chord changes, focus on your ring finger (start your "C" chord with Ring, Second and then Index) because it is a more natural flow with gravity and helps your fingers fall into place. Allow your fingers to follow what Nature gives. Many players fight what's natural before it becomes natural.
Let me know if this helps with your ability in those chord changes.