Coordination between the hands can take some time. I think a big help is to start very simple and work it slowly and often. Whether you start with picking out the melody for twinkle twinkle little star, or a simple fiddle tune or a scale. Start slow and focus on the quality of the notes. Play so slowly that you can really focus on where you place your left hand fingers (right behind the fret) and how you place them (use the tips, don’t apply more pressure than is needed). Stay on a particular tune for a long enough time so that it becomes committed to memory, then muscle memory. Don’t work on speed, work on quality. The coordination will generally come with repetition. I think it DrGuitar who likened the process to the tortoise and the hare… gong slow will get you to playing better much quicker than trying to play fast to start.
As you spend time playing your weak point will sometimes change. Today it may coordination between the hands, in the future, it may be your right hand or left hand technique. In any case, my best results come from slowing way down and focusing on that weak point.
Best of luck! Let us know if you find something that works for you.