I'm publishing in a field related to applied linguistics, and I'm making use of a new theoretical framework which has been used only in 4 published articles. 1 of those articles was published in an in-house university journal and the other in a very dubious open access journal, i.e. the kind of journals that publish basically anything.
Do I cite and probably critique these 2 papers in my lit review or ignore them?
I've certainly made use of these kinds of journals or conference proceedings in the past myself, which tend to have limited or no peer review. Those older papers of mine haven't really been cited by others, nor would I expected them to have been. But now I'm a bit further along in my career and publishing in journals with good citescores.
The articles aren't terrible, but somewhat misuse/misunderstand the theoretical framework I'm using. One in particular describes and tries to use the framework as if it's quantiative when it's actually qualitiative. I came across the papers late in the writing process, so I can't say they have contributed to my theoretical framework or analysis. I feel if cite them at all I'm giving them weight and weakening the impression readers would have of the framework. One of my main purposes in writing my article is to popularize the framework. I also don't think it's great to cite some obscure paper in a well-known journal just to tear it down.
What does everyone think? Is it better to ignore these papers, or do I have a responsibly to cite and critique all studies which make use of the theoretical framework, however suspect the publication source is? Obviously I'm leaning to the former, but I'm open to a change of mind.