I think a comfortable distance between the island and the counter is around 42". It seems that you have only 30" between your cook top and the counter. I might be a little too tight. The wall between the entrance and the kitchen could be 4' long instead of 6', you would then be able to move the island a foot which would give you more room between the cook top and the island. Could you switch the location of the toilet and vanity in your dad's bathroom so your enter facing a vanity instead of a toilet which is a lot nicer.

Do you have any photos or more info on your kitchen so we can help you?

I would consider putting cabinets on the short wall where the utility wall is. Have your stove there centered on the area. Move the sink so it is centered on the long wall where the cooktop is now. Put the fridge on the end run of cabinets closest to the dining table. That will give you an L shape kitchen with a nice work triangle. If you have your heart set on an island remove all the wall cabinets and install a large island. This is not the style of your kitchen but it does show the layout I described above. L shape cabinetry with stove on short end, sink in the middle with DW to right of sink with cabinet above it for dish storage and the refridgerator on the end run so it is out of work triangle and conveniet to the dining area for serving or work triangle for prep and cooking. Island can be any style you desire. L shape with island and open across from island; you might consider this layout if you desire an island. Something like this?

@Cornerstone design studio: Apologies for making big post; thought that more info will help. @Rupal ji, If it sounds like I dont need any changes; my apologies for that. Let me put it in short,"I am looking for options that give modern facilities without leaving good things from old charm/ comforts. " Thanks for the straight forward comments. I shall try to edit my original post to make it simpler and that looks open to new ideas.