What do you mean when you say that Skyline shows that the longer version of your missed cleavage peptide is not present?
Are you saying that no peak was found in the extracted chromatogram, or are you saying that the peptide did not appear in the Targets tree?
If there are peptides in your spectral library which are not appearing in the Targets tree, you can always add them by going to:
View > Spectral Libraries
and pushing the "Add All" button.
I am not sure whether there is anything that can be done about dealing with "Fixed Value PSM Validator" q-values. I am not the expert on reading Proteome Discoverer files, but if you send us all your data files we might be able to figure something out.
I am not sure which files we would need. Probably the .pdresult files and your .raw files, and you could also use the "File > Share" menu item in Skyline to create a .sky.zip file containing your Skyline document and supporting files including extracted chromatograms and spectral libraries.
You can zip everything up together and upload it here:
https://skyline.ms/files.url
-- Nick