Existing buggy code or a brand new one? (From time perspective)

Question

I am facing some issues with a buggy library I currently have and it's used in my current project, I need to finish this project as soon as possible in order to deliver it to our client.

However, this library is horrible!

Lots of bugs, lots of errors and bad performance, I thought to write my own library to handle what that library handles (GUI/Graphics and some Data manipulation) but I lack time to do it.

I have wasted a lot of time repairing this library thus I am very close to my deadline with 85% completion and still lots of bugs I face and fix everyday.

Maybe you will ask me the following question:

Why did you use it in the first place if you knew it was buggy?

I will answer that question, the reason why is because the buggy library is considered a standard in out company; plus, I am not the only one who thinks that library is buggy, almost all developers hates it!

My question is, should I deliver the current project with that library then develop a new library and use it to enhance the project after that deliver it to the client again as an update, or develop the new library and restart the whole project using the new one? and why?