Here are my recommendations so far:
Katie should not let on to the kids that she's a fluent speaker of Spanish. This way their lessons can be complete English immersion and the kids won't ask constantly ask for translations. She can do this by using lots of gestures, pictures, drawings, props, repetition, and cognates, and by acting things out or demonstrating. Oxford University Press makes some good picture dictionaries specific for English language learners, as do other publishers, but I suspect that most children's illustrated word books would also be useful.
Katie and Kirsten should set goals of what they want to accomplish, what they want the children to be able to do--talk about themselves, ask important questions, follow directions around the house, identify objects, listen to stories, etc. (Should she start teaching them to read in English? I don't know; if they don't read in Spanish yet, probably not, as we wouldn't want to overwhelm them. So then should they learn to read in Spanish? Help! This is beyond my expertise!) Each lesson should address those objectives and the kids should leave the session feeling like they've learned something new or understand something better.
Katie should vary the activities in each lesson to appeal to different learning styles and to accommodate the fact that seven-year-olds usually don't sit still very long. Including as many different kinesthetic activities, movements, and games will keep the kids engaged. (Click here for some of my homemade games ideas.)
Katie and their mom could pick out some textbooks and materials for English language learners at the elementary level; perhaps local elementary schools could tell them what they use in the different grades. Each child should have his or her own book(s) (rather than sharing them). Unfortunately I don't know enough about this genre to make recommendations myself. Anyone?
While teaching lists of nouns and verbs (to any age student) is very manageable for a good teacher like Katie because these words are easy to illustrate and act out, she should also familiarize them with function words like articles (a/an/the), pronouns (I/me/she/her etc.), interrogatives (who/what/where etc.), prepositions (in/on/near/to etc.), and conjunctions (and/or/if etc.). It's frustrating as a language learner to be able to point to objects and label them but not actually make sentences or express complete thoughts.
By the way, a book that has worked amazingly well for the little girls I tutor in French is called I Can Read & Speak in French: The Simple Picture Method for Kids to Learn French Immediately. It draws upon the Symtalk method where a usually-logical symbol represents a person, place, object, action, or idea. In this book, which also exists in Spanish and so probably in other languages, a sentence describes a photograph. Each word in the sentence is illustrated by its assigned symbol. As soon as the child can associate the symbol with the word, he can "read" the sentence, especially when aided by looking at the illustration. The goal is not to have them read, but rather use the vocabulary (composed of all the different parts of speech) to describe the picture. Eventually the child is able to tell the whole story of the children who go to the park with their bikes and dog and kites and end up falling in the fountain. It's very empowering for students to be able to tell a story in the new language! I also encouraged the girls to personalize, to tell me about when they go to the park, to describe their possessions, and so forth, using the same key vocabulary and the included flashcards. All this took, of course, a month or two of going over the new words little by little, reviewing the previous ones, playing games like Memory with the flashcards (I also made bingo cards with them)--it doesn't happen all at once. And the Symtalk method becomes increasingly more complex and can be used with many different levels and ages, but I don't know much about it beyond what I've seen with this book and at one conference session where the presenters showed us a lot of advanced Symtalk games. The book I describe here also comes with a CD, stickers, and directions. Here's a sample vocabulary page and one of the story pages:
If Symtalk books like this for ESL children don't exist, perhaps Katie or Kirsten could create something similar, using pictures of the family and their home and their possessions to tell a story.
The parents and siblings should reinforce at home what Katie covers in the English lessons, but also expose the children to songs, appropriate television programs and movies, lots of books, magazines, and poems in English, and interactions with other kids at home, on the playground, at playgroups, perhaps something like a music or gymnastics class.
Katie and the parents should check out the websites TESOL/ESL/TESL Resources and Colorin Colorado, too.
I recognize that so far these are pretty general guidelines. I'd also like to be able to suggest some specific activities that Katie can start doing the first day she meets with the kids. If you have any ideas or comments, please share them with us!