Apartment renting question

I'm mostly posting this to make sure I'm right in my thinking here. My girlfriend and I currently rent from a rental company and they've been a bit of a nightmare. Rent is never taken out on time, and it being extremely hard to get any communication with the building manager are a few of the reasons we want to move.
Just recently we signed a new one year lease with them because by the time we were told they offered month to month, it was too late to write up a new lease as they had already written up the year one and it was a day past the due date anyway. We renegotiated our rate and got it lowered a bit. On September 1st, rent wasn't taken out. That's not unusual for them. On September 2nd they took it out but at our old rate. They've also not provided us with a copy of our new lease and it has now been 21 days since the new lease was signed.
I know them not providing a copy of the new lease only allows us to withhold rent until they give us a copy, but my question is, does them taking out the wrong amount(our old rate) count as them breaking our lease terms? And because of that, can I safely serve them with notice that we'll be ending our tenancy without penalty?
Thanks for your help.