I agree with you that your therapist is not providing you with the security or service you are looking for in having someone available when you have signed on with her to be your therapist.
Being late for you appointments is something I would certainly address with her although I know this will be hard. Also the cancellations.
My Pdoc has me assigned to 20 minutes and I better be on time or I could be down to 10 minutes. To cancel an appointment I must do so at least 24 hours in advance or I am automatically charged the $248.00 for her services. No reason is good enough to cancel after the 24 hour mark. Ugh.
IMHO patients are due the same respect as the therapist or physician. As you have only been seeing her for a few months and you "have grown frustratied " it feels to me like you may be losing your trust in her also.
I would look at what you feel will best meet your needs.
Take care and know we are here to support your decisions.