First, I wouldn't put credence into what other riders say per se. This may sound like sour grapes on teens but some just can't help but give their opinions especially when they have a high opinion that they are better riders than everyone else. We have teens at our barn who were banned from the barn for a full month due to their constant bullying, harrassing and criticism of other riders. They weren't just doing it to the younger kids but to adults as well. Your instructor/trainer should be your guide. If the instructor felt you were ready for the mare than go with it.
As you pointed out, it could very well be that because you were correcting the mare's poor behavior she was throwing the proverbial temper tantrum. Sure, anyone else may get on her and let her get away with everything but it doens't help the mare in the long run and certainly doesn't work to correct the mare's issues. It also doesn't improve the other riders' riding ability..it makes them a passenger, not a rider. The fact that you got back on twice and even finished with jumping, even simple crossrails, tells me a lot of your mettle.
If you ride this mare again, think of more subtle means of correction. Some horses just get stupid with a crop. Force her into a circle, as tight as you can get, make her work hard when she acts up. Eventually she will figure out that kicking, bolting or being an obnoxious so and so isn't worth the consequence of then having to work three times as hard. Plus, in a circle, she can't kick, buck or bolt.
An example...my last horse had a serious problem with standing at the mounting block. On the very first day after I bought him, it took me 15 mins to get on him. Why, because every time he moved off I forced him into a tight circle and made him move his feet by making him give way with his hind quarters. It may have taken 15 mins but he eventually stood still and never again in 5 years moved off from the mounting block without my giving the signal.