Many of us including myself tend to throw technology at problems that otherwise would yield better and optimized results by old fashion human intervention.
The problem as I see it:
You want to present to the coaches and team information that will allow them to make decisions on how to improve their performance on the ice during a competition. Simply, you need an accurate and clear recording of a game with the best possible details of the actions of all the players engaged with the puck.
While it would be nice to have two cameras to cover the entire field there is still the problem that the optimal portion of the screen will be the half way point between the goalie and the center per both cameras. Any action at either goal or center will be on the edge of each camera's frame. This is not optimal. The best solution would be for one camera to "follow" the action with enough detail to capture the players handling the puck.
Consider how professionally produced hockey games accomplish this by using the following: multiple cameras at strategic locations fed into a live mixer and switcher under the supervision of a video director, and yes with the occasional cut away shots to the commentators. Not to mention the real time graphic compositing with clock, scores, and handy info found marching across the ticker.
Let's streamline this to be affordable and targeting the coaching staff's criteria.
One camera with an experienced "sports" camera operator. The camera should have the ability to zoom and easily be focused manually on the fly, mounted on a heavy duty tripod with a very smooth fluid head and stationed on the center line of the field at 10 to 30 feet above the ice on the most stable platform. The elevation of the camera is critical to capture the geometry of motion under play.
The camera operator must be extremely experienced to achieve the optimal recording. Hiring a student with little or no live sports coverage experience and expecting the student to yield professional results is at best a fairy tale. One of the most demanding and challenging camera work is sports photography. So don't even think about skimping on experience here as you have already found out it will bite you in the butt.
You likely do not have a budget for hiring a professional camera operator.
No worries, since this is a high school you have an enormous resource of moms and dads, uncles and aunts, or other relatives that may have this level of experience and are more than happy to volunteer their skills and talents to assist in improving the performance of this hockey team. Imagine if you had a son or grandson involved in hockey and you are both proud of this and love the sport, and were once a professional sports camera operator.
You only need this experienced person for at least one season as they train two student interns who are at most in their junior year or one year from graduation. You should have at least two interns so you have back up.
These interns should first demonstrate a keen passion for sports video capture and they should receive academic credit for their efforts and perhaps some tuition weaver or discount as an additional incentive. These interns should be additionally trained on the care and feeding of the camera, tripod, and any associated accessories.
In the following year the former interns will be your mentors for the next batch of interns.
Now you have a sustainable means of professional quality capture and recording.
I base this answer on personal experience some 40 years ago.
While I was in my senior year at SIU Carbondale as a cinema major, I was selected from numerous applicants to a special internship for credit to the SIU film unit. One of their main duties was to record on 16mm color film all the home games of the SIU Saluki football team. I recall many Friday nights and Saturday afternoons working as camera assistant to a professional camera operator covering these games. This guy had it down cold with numerous seasons doing this. He would demonstrate technique and then I would have a chance to see if I had got it with his evaluation right on the spot. Instant feedback, instant progress.
One camera, zoom lens, heavy duty tripod with a very smooth fluid head, mounted above the press box outside at about 60 to 80 feet centered above the 50 yard line. These films were absolutely needed for the coaching staff. This coaching staff expected professional results and they got it delivered. Hence, some of the funding for SIU film unit thus came from the SIU football program.