Instruction Advice

I took my first swim lesson the other day (at age 33) so that I can learn if I would like to incorporate swimming into my regular exercise regimen. I am not entirely sure how to assess my initial lesson in terms of instruction received and I was wondering if anyone had any advice. She had me swim one lap to take a look at where I am today. She commented very quickly that my hips sink and they don't rotate. I can't breathe properly, which leaves me very gassed by the end, so she had me breath every other stroke to my 'favored' side in an effort to keep me from thinking about breathing and to get me to think about my hips. She had me do 2 laps swimming, 2 laps kicking with a kickboard, 2 laps with a pull buoy, 2 laps of side kicks, 2 laps of backstroke, one lap of 'alligators' (head out of water looking straight ahead and forcing the hips up as much as I could). The only thing she commented on during this first lesson was that my hips sink and do not rotate, and so with each exercise, that is what she wanted me to focus on - including the backstroke, where she thought it would be helpful for me to get a feeling of floating and getting my head down, with very easy access to air to breathe. Luckily, I won't be getting another lesson for a week and a half or so, which will give me some time to go through a workout she wrote up for me (pretty similar to the above) and try to gain some comfort with the water. At any rate my question has a couple of parts. I liked my teacher, but I do not know really how to assess what we did. Was that sort of workout the general type of early lesson stuff people do? Is getting my hips up a good early thing to focus on? Are there specific drills I should think about, or are the drills she did with me good. Will getting my head down push my hips up, or do I have to 'will' my hips up by flexing the muscles in my midsection (front and back). I realize this message is lacking in a good point, or a good specific core question, but I think that sort of describes my whole ability at this point! At any rate, I thought I'd share that to see if anyone had any advice as to how I might best prepare myself for my next lesson, and how I can judge whether this is a good instructor for me (She is a nice person, and we get along, so that part is in the bag). Thanks.