My answer is just an affirmation of what you are wondering. Yes to stain cpDNA using DAPI, you need to isolate the chloroplast first, and this I can say by my experience of isolating protoplasts and chloroplast for my fluorescence microscopy experiments using several dye. DAPI has high tendency to bind with the condense DNA, so once it enters a permeabilised cell it binds more to condensed DNA (nuclear) compare to RNA or cpDNA. So most of the fluorescence we get, comes from nucleus which overshadow the fluorescence coming from other part. Also the large amount of compact nuclear DNA compare to dispersed cpDNA in the cell, is another factor that make the DAPI signals coming from cpDNA week to be detected.