I’m almost certainly not the best person to answer this question, but you’ve been waiting a while and I’d like to at least get the party started.
Disclaimer: I have no experience with this, and am just exploring the documentation to try to help describe the problem and work toward a solution. Please take my words here with a of salt.
First, can you give us more information about your situation? For example, what does your prep and sequencing process look like? What amplicon are you targeting? Why are there adapters inside your sequences? Is this expected based on your protocol, or the result of an error in prep? Are you sure you want to keep the bases on both sides of the “stranded” adapter?
For example, the cutadapt docs talk briefly about one way in which adapters can occur in the middle of reads (long reads, short space between primers, if I’m reading it correctly). If that’s what’s going on, you might not want the excess read outside of your primer pair, as that data would not be a part of your target amplicon, and cutadapt (or q2-cutadapt) will happily lop it off for you.
I’m trying to retrain my habit of novel-writing here on the forum - maybe let’s start with those questions for now, and go from there?
P.S. The q2-cutadapt docs do a nice high-level job of explaining how that tool works, and are well-aligned with the options available through the cutadapt tool itself. While reading the cutadapt documentation, I found it helpful to back and forth between them a bit.