I'll put on my "I used to work in PR" hat.
Have you talked to the reporter and team about what sort of story they are after?
A quick conversation about what kinds of things they would like to see and what kind of information they are after would give you a sense of what kind of direction to take and if you listen carefully you can probably get a sense of the level of info the reporter already has and if there are potential biases.
You can also ask if she wants you to send her any background (the mothering mag article from a couple of years ago is a good neutral backgrounder).
Your kids are young - and that can make for unpredictable tv. I'd do a lot of prep work - make sure they are well rested, well fed, that they have an understanding about what the crew is there for, that there is a partner/friend of yours there who could entertain them if need be.
I would also have some things set out as triggers for them and you to talk about.
A photo book of a recent trip, a favourite game, a science experiment, an interesting pet, their corner of the garden, their art journal, a collection of something interesting, their judo uniform or swim badges. Is there some project or passion you are working on together that would illustrate unschooling positively? I'd have some visually interesting educational activities out for you and the kids to do as well which will give the camera good positive images to lay behind your voice if need be - pattern blocks, drawing journals/water colours, musical instruments, microscope/magnifying glass, puzzles, bug jar etc. The camera crew will use what they see to set up shots so if this sort of thing is readily available then it makes your job and theirs easier.
I agree with the PP to practise practise practise. I would write out your philosophy about why you choose homeschooling/unschooling and refine it so that it is concise and clear and non-negative. I would come up with a list of anecdotes about your kids and how they have learned something naturally or been engaged in a passion, about how they are engaged in your community etc. I would think of the top 10 objections to unschooling/homeschooling and again write out answers to those and refine them so that they are clear and positive. Read them and practise saying them so that the answers become genuine and the phrases you want to use become second nature to you. I'd suggest having someone who is homeschooling neutral listen to what you say to see how it comes across.
Be well versed in your local laws and some of the statistics about homeschooling in the US. Be ready for the "college" question with some stats and anecdotes. The socialization question is likely to come up. I'd make the case for clarifying socialization from socializing and have examples of your children's opportunities to socialize.
I would try to keep answers short, concise and clear. Rambling answers can be edited in such a way that the context is lost. If a question is framed in a negative way, answer the question that you wish the reporter had asked. Ie if the question is "aren't you concerned that your child will never learn how to get along in society?" reframe it so that you answer the question "How are you ensuring your kids will learn how to get along in society?". This does a couple of things - it stops you from answering a question starting with "No...." or "I'm not concerned about that...." and it keeps things more positive and proactive and keeps you in control of the answers you give. You can even say at the start of your answer "OH are you asking how we do ABC?" and answer from there.
If you sense that there is some bias from the reporter or the interview is heading in a direction you would rather it not go, a good strategy is to find common ground with other more readily accepted ideas. You could for example use other educational philosophies to help frame unschooling. There are parallells between Montessori, Waldorf, Reggio and even main stream schooling which can be used as a stepping stone to explain unschooling. Things like prepared environment, using inquiry based learning, respecting the child's developmental stage, building on passions, small group learning with an engaged adult, hands on learning, community based learning are all things that make sense within the context of many educational philosophies. You can also talk about how unschooling is akin to how adults learn - finding an interest, finding resources, and delving in until they are satisfied.
I've got to run - hope this helps.