Some schedulers are terrific, some not so much.
Frankly, there are some schedulers whose e-mails I automatically delete. I won't work with them (for exactly the reasons you list), so I don't even bother reading them.
You're an independent contractor. Going over the scheduler's head is poor form.
I do overlook the occasional lapse in manners or responsiveness. Sometimes, life just gets in the way, for schedulers as well as shoppers.
I'm still irked at one scheduler who answered my e-mail with "But it's the weekend! I'll take care of it Monday." While I'm out Friday night, all day Saturday, and Sunday, working my you know what off. What's a weekend, anyway (to paraphrase Violet).
Sorry. If you expect me to work over the weekend, you'd better be available to answer questions!