Kelly, have you worked dk before? (I haven't yet, but am, among other things reading about it right now. So if anything here sounds really idiotic here, that's why.)
Having mentioned that I've not yet personally done dk myself, perhaps what I have learned by research might be useful to you, even if you do have some dk time under your belt. Or maybe this thread will teach me, or perhaps both of us, something along the way.
I came across the About.com heart pattern Amy uses in the video and the instructions at About.com totally blew me away. See a final note about this in the 2nd last paragraph, as this "little detail" so casually referred to over at About.com is one of the "little very important things" that distinguishes this web site from all others. For the reason explained near the bottom of this message, I'm really glad Amy used the pattern in her video, since it gave me an even greater appreciation for this highly informative website.
If you noticed in the video, she holds up the work and expands the body of the piece, showing that it is an open work tube. The sides, bottom and top are closed. If I understand correctly, in dk there are 2 basic types of tubes, open and closed work. I believe the pattern called for a cast on that closed the bottom end.
I took a look at the hat pattern in question. In the opinion of this novice, it looks like the pattern calls for an open work technique for at least the top part, judging from the description of how it's closed.
Assuming it's a closed cast on, the Row 1 & 2 instructions have me a little confused at the moment (i.e.- just how the heck does she expect you to rework the same row if you don't turn?!) I would imagine a lot of people would start wondering if there's another way to work the pattern after seeing that first set of instructions.
In answer to your question about circulars, considering they are called for in the pattern and some personal experience working circulars as straights, I wouldn't think circulars would make a difference either. The pattern instructions, however confusing they may seem to me at the moment :?? do indicate where to join and start working in the round.
Perhaps you weren't thrown so much by Row 1, as by Row 2....uh, like how am I supposed to slip a color I haven't even picked up yet? So your question about working both strands in the cast-on make a lot of sense to me!!!
So now that I've shown the world just how ignorant I am about dk, I'd like to make amends by suggesting to you (and others) what I am about to embark on myself. Aside from writing here, I'm working a few small projects for the upcoming holidays and yet to really sit down, absorb and work through the following EXCELLENT resource.
I would suggest taking a look for what is considered the consummate resource on the topic of DK, created by a person who has been described as an absolute genius on the subject. The story of how she developed her techniques in the Introduction is incredible and, well worth anyone's limited time to read it. I highly suggest you look for "Notes on Double Knitting" by Beverly Royce, from Schoolhouse Press, edited by Meg Swansen. This is a book worth reading from front to back.
I mentioned the book to Amy a few weeks ago and promised to get back to her about some details in the book, once I've absorbed it. Apparently Amy has met Meg and had some sort of discussion about rare books, like the one to which I refer.
Since the book is out of print and you're likely to fall over when you see the price at the few places you might find it (even on ebay); I highly suggest you do what I'm doing, check your local library and interlibrary loan for it and make a copy. I promise you, you won't be sorry.
From what I can already see, this is an invaluable resource on the topic. In fact, I've never seen any book quite like it on any subject. I cannot for the life of me figure out why this book hasn't been reprinted?! Though Amy reassured me that there are some others out there that are even more rare and pricey.
Judging from a very quick reference to this book, which I'm privileged to have on loan (there's only 1 available copy in my entire state), it appears the Row #1 technique being described is called "Pattern Stitch #3" on page 15 of the book and is worked from the front side. On the same page, Row #2 is referred to as "Pattern Stitch #2" and is worked from the back side. Each of these stitches work the tube right side out, which makes sense as the hat's picture looks like stockinette (as does the heart pattern in the video).
Each of the methods in the book describe a cast on for working a closed tube, with a cast on of either your regular one, used in straight knitting or an invisible one. 2 different methods are included on pages 17 & 18 of the book. I'd say an invisible one is assumed in the hat pattern? A provisional cast on is casually mentioned at About.com (and a LONG search of the site for it provided very unhelpful information, leaving me even more confused), and blew me away so badly, I could only hope to find a better explanation of the pattern and technique elsewhere. Note to pattern instruction developers/contributors: As much as we really appreciate your kind service, never assume your users assume to know anything ahead of time. Make it clear what you're doing and HOW, by providing a few links to the additional building block skills which may be necessary to get the job done correctly THE FIRST TIME!. [HUGE sigh] Oooh, I feel so much better now, thanks for letting me get this off of my chest!!!
Gaaawd, I hope this long message is at least somewhat helpful for you!