What kind of chords are you trying to play? As you are a beginner I'm thinking you are not trying to play barre chords yet. As with any new skill you learn, sorry, it does take time and practice. When you bend your fingers they naturally will be closer together. A lot of guitar is built on muscle memory, which basically means you have to train your fingers to go where you want them to. Also keep in mind a smaller guitar does not mean it has a smaller neck. Perhaps the neck on the guitar is too thick? As far as exercises, just try walking your fingers up and down each string (one at a time) and just keep telling yourself, one finger per fret. You'll get there, just keep at it and if you get frustrated, that's ok, just put it down and try again later. Even 5 mins here and there is going to help. Don't even worry about your right hand or getting the chords to ring out at this point just get your left hand sorted out and the rest will follow.

Good Luck!