Everything you are looking for is right here on Earth?
Limpets are a real life organism that contain what is perhaps the world's overall strongest biological material. Thier teeth are made of an iron composite based crystalline nano-fiber called goethite interwoven in a special protein matrix which together give the tooth an unprecedented combination of both hardness and toughness. Thier teeth have an even higher ultimate tensile strength than spider silk, they are highly resistant to impact and shear, and they are ridged enough to function as teeth... so a similar material could certainly be used to reinforce a skeleton.
If you specifically want chiton that contains iron, gumboot chiton is an iron rich chiton used in the teeth of meatloaf mollusks. Not quite as tough, but still a very impressively strong material.
Why isn't goethite more common in Earth based animals?
Bones are more than just a a framework for moving around. The minerals in our bones are designed to be reclaimable during times of malnutrition, pregnancy, and healing to help keep our bodies going. Calcium is an extremely important micro-nutrient used by animals in over 100 different biological processes, but is a relatively rare element in nature making it especially important for animals to stockpile. While iron is also useful in many biological processes, it is very common in nature; so, it is much easier to get on an as-needed basis.
Without calcified bones, starvation and cellular malformation would be a much bigger cause of death than bone fractures. Calcium is also much less dense than iron which is important for any animal that plans to walk, swim, or fly. So, there is a big evolutionary pressure to favor a weaker calcium hardened bone or chitin than a stronger base material like iron.
Would strong tidal forces cause iron bones?
Probably not. Iron bones would make you more dense which means aquatic life would be less able to float. Such animals would be more in danger of being dragged along the seafloor by the tide instead of swimming over the dangerous ground below. Instead, you should focus on biochemistry and gravity as the influencing environmental factors.
If your planet has a lot more natural calcium and less iron, then your organisms would be more inclined to sequester iron in thier bones and treat calcium as an on-demand micro nutrient instead. Also, a reduction in gravity could make the added weight of iron less of a disadvantage.
If both strong tides and iron skeletons are both essential part of your setting, then you should certainly keep them, just be mindful that one does not cause the other.