In spite of knowing the warnings against making assumptions, I'm going to base my answer on the following assumptions:
1 - That if she had said "Booked" and nothing more after you enthusiastically responded "Ok, see you then [Saturday] anytime!" you would have interpreted this to mean that she was arriving on Saturday;
2 - That your "specifying" that "anytime [on Saturday]" would be fine for her arrival meant that the time of her arrival was a fact that you deemed important enough to discuss; and
3 - That you knew that she was not planning on both arriving and departing on the same day, be it Saturday or Monday.
With these assumptions in mind, I agree with the other answers given so far that the scenario you present totally justifies her belief/interpretation that she would arrive at the destination [at anytime] on Saturday, stay there for two nights, and then depart from it on Monday.
Regarding assumption #1, you apparently interpreted, as she did, the "make it" to mean "arrive at the destination," which is the normal, perhaps even the only interpretation of "make it" in this part of the exchange (whereas your later interpretation of "leaving" to also mean "arrive at the destination" [after "leaving" the point of departure], is not, however, the normal interpretation of "leaving" in this or any other scenario, and your rather convoluted interpretation of "leaving" was, IMO, the SOLE source of confusion and ambiguity in this exchange).
Regarding assumption #2, in your simple "OK" response to her "leaving" on Monday you failed to make any mention or inquiry about what her "arrival" time on Monday would be, which was inconsistent with your having been so careful to let her know that "anytime" would be great on Saturday and which supports her interpretation of the total exchange.
Regarding assumption #3, if you knew that she would not be leaving the destination on the same day as her arrival at it, it seems that you would have expressed at least some interest as to how long she was planning to stay and your failure to do so further supports your would-be guest's interpretation of the total exchange.
I really don't see any ambiguity arising because of "will" taking precedence over "can" unless you can honestly say that the entire mess could have been totally avoided if she had simply started the exchange with "I'll (be able to) make it on Saturday" instead of "I can make it on Saturday."