I do not know of a tool with such functionality built in, but with automation (using a tool like iMacros or Selenium), you might be able to obtain the result you seek. (Unfortunately, it is beyond the scope of my answer to explain how to use such a tool, so I understand that my answer might not be useful if you do not already have such skills and are unwilling to learn them.) The procedure might be something like this:
- Navigate to a web page with the full list of references of the article whose references you want to search. This should be in a full text database like EBSCO, ProQuest, etc.
- For each listed reference, use the automation tool to copy the title, authors and date of the reference.
- Use the automation tool to search for the referenced article in the database. If you enclose the title in quotation marks, the first article that comes up should usually be the referenced article that you want. But you should use the automation tool to record the full citation details of this first article so that you can manually verify later that it is indeed the article that you wanted. (This latter step is important!)
- Use the automation tool to click on the first article that comes up, then search for the words you are looking for.
- Use the automation tool to save whatever results you want.
- Finally, double check the list of full citation details of the articles that the automation tool actually searched on (that is, the first one that came up for each search) to make sure that they are the correct articles you intended from the references list. Whenver you found that the automation tool guessed wrong, then manually search for those articles.
Again, this answer only helps if you know or are willing to learn automation tools. (If you do choose to learn a tool just for this project, you will probably find that it opens new opportunities for lots of projects in the future, so it might be worth your time.)