Buy your own Scotsman Pellet ice maker. They are very expensive but the if you consider the amount of time and money that you are using just to get the ice (then transporting and storing.) It might be an opption worth looking into. Plus, that would be so cool to have it on hand whenever you want! Fresh, no melting, and no hard re-freezing.
Or you can learn to make ice like it at home; as I have. This may not be right for you because you and your wife are chewers and it's not easy to make in large batches but the recipe is called 'sonic like ice' on the recipes section.
Until you find another way you might just have to get coolers and start getting ice once a week. Get as much was you can fit in the coolers. Then you could use cold salt water on the way home to keep the bags from melting than refreezing once you get them into your freezer. Salt water can be colder than frozen ice, so using regular (none sonic) ice plus really cold salt water in your coolers on the way home should help. Less trips more usable ice and you would only need the coolers in your car for the trip. Also, check the defrosts on your freezer that might be making the ice melt too much.
Good luck! Hope this helped! Happy chewing.