IF you have proper Iodide and IF you have proper Iodine then it is normal for the Iodine to take a long time to dissolve.
the proper way is to sellect your bottle. lets make it a liter. lets make 5% lugols. put your 100mg of KI in the bottle. add enough distilled water to dissolve the KI. should be no more than a quarter full. at this concentration of KI the Iodine will dissolve instantly. add the 50mg of iodine, shake and fill to the top with distilled water. all done.