Knowing the halogen content of the naturopathic remedy is good, though it sounds like the systems behind the mineralization systems and fatty acid intake might be needing support.
Ideas are mixed (about ingesting dairy among health gurus), but some source of long-chain fatty acids is an excellent idea, (organic grass-fed dairy is one), and a good source of silica and organic calcium (like eggshell powder, easy to make at home).
Horsetail herb tea is very high in useable silicates (bound with phosphorus), but you'll need to drink a good amount over several months.
If you live on low-calcium soil, it grows very well. Do look up google image results of it, and check your local weeds. ;-)
Diatomaceous earth is a good supply of silica too, and helps strengthen and cleanse the intestinal tract for better nutrient absorbtion. I just reccommend starting at a low dose 1/8 tablespoon/day instead of the common 1 tablespoon per day, to find out how much your body can tolerate in the beginning.
My favorite Iodine source is kelp from a good seabed, or Black-Walnut husk tincture. Straight Iodine can be a heavy detoxer, but transdermally across the sole of the foot it's really good and gentle (if you choose to buy something like JT Crows Lugol's iodine).
I mentioned halogen content because there's four halogens in the body - bromide, flouride, iodine/iodide, and chloride (healthy, chlori-ne is the unhealthy one). Weak teeth and nails can be a symptom of a thyroid that needs help, and if you're in the states or a country which uses bromides in the textile/food industry, and chlorine and flouride in the water supply, it can have a meaning for your well-being (iodine is one of the main constituents of thyroid hormone).
Flouride is used in general to harden tooth enamel in standard toothpastes, but it's considered in the naturopathic community to be something that makes the bones and teeth quite brittle. Black teas and coffee can be a heavy source of flouride, so do consider your everyday habits.
The the first halogens (bromide, chlorine, flouride) can have a displacing effect on iodine when consumed on a regular basis. (This does not include salt on your food, sodium chloride. Chlorides are good and necessary for brain function and the immune system)
If you're suffering cold hands and feet, sluggishness, a strong appetite for carbs and tend to gain weight, thyroid support might be the way to go (NOW Foods makes a good one).
Otherwise, go after silica and selenium-rich foods, and the healthy fats. ;)