I also think that the timing of the return call was a coincidence. During June and July, the clubs have meetings to go over the information and guidelines issued by the USFSA. The USFSA has issued guidelines and held online conferences/training to roll out this initiative over the last month since the new membership year just started in July. (Which reminds me - make sure your daughter's membership for 2013-14 is renewed ASAP.)
At this club, they no doubt met to discuss the upcoming competition and the new SafeSport coordinator explained the rules to the competition director. In May, our brand-new competition director was unaware of this rule and another club's director brought it to the Club's attention. The director had to scramble to comply because our club has NEVER credentialed coaches for competitions. It was a learning experience.
This "registered coaches only" issue has come to head over the past few weeks with the training for the new SafeSport initiative - it really drives home the point that clubs have to start enforcing the rules about who can be in the coaches' areas during tests and competitions. The brand-new SafeSport Chairpeople were told that it is THEIR responsibility to verify coaches' compliance and have ice monitors police the coaching area for credentials. It's likely that the SafeSport person corrected the competition chair.
Several coaches and board members have said the same thing about the timing of the return call. Don't assume the coach is maneuvering against you. That said, it sounds like you don't care for the coach's style because you've painted her to be a controlling, manipulative shrew. I think you're being unfair, but it's probably best if you change coaches since you distrust her so much. You should talk with the coach and tell her why you want another coach for your daughter, then approach someone else to do a few trial lessons.
As for the other parent ignoring the jump coach in favor of hiring a stranger to save a few dollars, be an adult. Ask the jump coach what the cost would be and discuss what you've budgeted for this fun competition. It sounds like you're going off half-cocked and making assumptions that may not be accurate. By the time you pay for an intro lesson/coaching presence , you'll probably be paying $30-40 for a stranger to put your daughter on the ice. If the jump coach, who knows your DD, can do it for about the same cost, you're slighting the jump coach.
Amazing that these scenarios are coming up at the Basic Skills levels. What drama will unfold if your skaters go beyond the basic skills level of skating?