My ward, a 9 year old girl, has been told by her coach that figure skating will ruin her hockey technique. She received some figure skates from my mother this past christmas and she does not feel comfortable using them now.
From my perspective, if a 9 year old little girl wants to figure skate because she is interested in the acrobatic elements of the sport, and STILL wants to play hockey, then I think this is fantastic! How do I reassure her that her coach is wrong? Is there any evidence to suggest skates with toepicks will ruin a defensewoman's skating technique? If anything, I believe figure skating will enhance her confidence on the ice as well as improving her agility.

No, figure skating doesn't ruin ice hockey technique and visa versa. In fact, they enhance each other! Our hockey director has complimented my daughter's (16 yo) skating skills many times. Her figure skating coach and the judges for USFA have formally commented on how the hockey playing has helped her edge work! She's been playing for 3 years and figure skating for 6 or 7 years! Of course, hockey coaches (especially males) don't always want to listen. THey tend to be opinionated on the subject. Just do whatever your daughter wants. Figure skating is hard work, too. Hope that helps!

Actually, I wish all the girls in our program had had the benefit of a few years of figure skating before playing hockey. Most of our kids, because the hockey program itself does not emphasize skating enough, have a variety of flaws in their skating technique and, as a result, don't get as much out of their skating as they could. The ones who participated in the local figure skating have invariably better edging technique, which is critical for starting, stopping, and turning effectively. They also come into the hockey program with competent backward skating technique. The one area where I have seen the former figure skaters having to adjust is that they tend initially to play out of a very erect stance, and need to develop the proper ankle, hip, and, especially, knee angulation to really develop power (which they invariably do). My daughter, a former figure skater, plays defense and her training in figure skating has helped her enormously. The transition from figure to hockey skates turned out to be relatively easy, and I know of both boys and girls from figure skating clubs here in Colorado who figure skate and play hockey in the same seasons and who have been successful in both.

If switching from figure skating to hockey, can anyone recommend a hockey skate that supports the ankle a lot...to ease in the adjustment of changing skates?

Pretty much all hockey skates have more than enough ankle support, especially if you lace them up to the top tightly. However, you want to be cautious as forward ankle flex is important in proper stride.