There could be a number of possibilities for double sequence in the PCR products. Since this has been your stopping point in the experiment, can I assume that the products have not been cloned into a vector? I know you said that you have been successul with Sanger sequencing on previous samples. However, you did not say these problematic products were cloned and sequenced.
Starting with the more obvious cause, you might be amplifying multiple products. It is also important to note that multiple products of similar length may not separate by agarose gel electrophoresis and therefore cannot be seen.
Another possibility is that the exosap may not be working. Do you have any control sample that will allow you to test the exosap. In this case both PCR primers would be present in the product. and amplify in the Sanger reaction.
It is also possible that the conserved region is not actually conserved.
I have also seen cases where one of the PCR primers (or both) may have multiple sequences. It would only require that some of the primer in the mix misses one base. Amplification of multiple products would produce double sequence where one sequence was different than the second sequence by one base. This would depend on whether this pair of primers had been used before.
This is a couple of possibilities. I will let you know if I can think of others.