I suggest simply:
Some employees of Wendy's are happy.
to avoid the problem altogether. Otherwise, I think it would have to be "Some of Wendy's employees are happy" (to be possessive) and that does give the impression that they are employees of Wendy, not of Wendy's the company, as you say.
That said, the possessive of McDonald's is frequently referred to as McDonald's https://www.google.com/search?q=%22of+McDonald%27s+customers%22 (but mostly by journalists and not by McDonald's themselves).
For example http://www.huffingtonpost.com/2013/01/18/dissatisfied-mcdonalds-customers-return-fast-food-loyalty-survey_n_2504951.html:
...22 percent of McDonald's customers said...
Perhaps that is simply because McDonald's is so famous that nobody is concerned about any misunderstanding that that means "the customers of McDonald". However, originally, it would have meant "the customers of [the] McDonald [family]" so it is not completely misleading if taken to mean that anyway.
I think the rule would be that, as McDonald's is already a possessive, no further apostrophes are needed to talk about its possessions. It can be read as meaning something slightly different to what is intended now that the possessive is a proper noun in its own right but
McDonald's' would be regarded as wrong so it's the only option there is (or to avoid it by using McDonald's as adjective rather than possessive).