I suggest you use a vocabulary based book and a conversation book in your classes. You could try English Vocabulary in Use (I think published by CUP). It’s similar in layout and approach to English Grammar in Use. Vocabulary is presented by theme; jobs, hobbies, environment, restaurants...... Basically the traditional topics. The language is explained simply and in English and there are exercises to practise the vocabulary in a written form. You can then initiate discussions around these exercises. You could use a discussion book for this; e.g. Discussions A-Z, or any other that you find on internet. Link the theme of the discussion to the vocabulary presented and she’ll get plenty of opportunity to use the new language. Remember to recycle new vocabulary; build in revision of previous lessons either through homework, written exercises or further discussion. You can also ask her to create sentences using the language and design crossword puzzles. I know what you mean about using games; it does seem unusual in a one-to-one setting with a middle-aged student.
Finally, I suspect that once the summer season is over, she will be open to other topics as she will be less absorbed in her hotel guests. If she expects you to present language in a traditional way, you can just go with the flow. At least you’ll have a happy student!
All the best