The problem with the above is not the extra conjunction. It's the logic of the sentence that's messed up.
I would rewrite the sentence in the following way:
Let's wait until my mother arrives. She'll have some money and I'll be able to enter the building.
But to answer your question. Yes, it is possible to have more than just one conjunction in a sentence.
I was late for work because it was raining and the traffic was heavy.