Do I have any legal recourse regarding apparently conflicting patents? How?

The answer to your question is very fact specific and will require a review of both patents and the products being sold by your competitor. But, in principal, if you have a utility patent that "covers" their product and you in fact have priority over your competitor's version of your invention, you should have the full gamut of legal remedies available under US patent law. The difficulty is usually in making sure your patent actually "covers" their product. Furthermore, there may be ways to invalidate their patent if in fact your patent application anticipates their patent, or if your product or the disclosure of it was publicly available prior to their patent application priority date. We would be delighted to advise you if you need further assistance. Initial consultations are always free.

Your writing sounds confused. You say someone has a design patent reading on your utility patent- this makes little sense. If this company has an interfering patent, and if there is significant value at risk, then you should engage a patent attorney. Based on what you say, I do not think you can handle this yourself. A good patent attorney can appraise your situation and advise you on the best course of action. Good luck.

Talk to a patent attorney. See if your utility claims actually cover the design patent and the product sold under that patent. If any "single" claim element in your invention is missing - the accused product does not literally infringe. Then check the "doctrine of equivalents" - is the accused product essentially the same as yours, doing the same thing your does, in substantially the same way? If not - then the accused product does not infringe under the DOE. If you find infringement - you will need to sue in Federal Court. There are some companies on the Internet that will sue for you - taking part of any recovery from the infringer.