This one is really pretty simple and the key is in your first sentence.... your mother co-signed for a car.
This makes her the secondary guarantor of the repayment of the loan. The lender has no obligation to pursue the primary borrower (your niece).. they can (and apparently did) withdrew the available funds from your mothers account. No notice required. And she (not you) can initiate action against the niece to recover her damages. Now, with that out of the way, we move on to your loan.
Already aware that your niece was a deadbeat (after all, she had already stuck your mother with her bill), you went ahead and loaned the niece MORE money on her promise to pay. And, with her verbal promise at that!!! Now, you are wondering what you can do to get your already-known deadbeat, no account niece to repay you. My answer, not much. Here are your problems:
1) Assuming you can serve your niece with legal notice, you can sue her in Small Claims court (if your amount is within the jurisdictional limit).
2) If you win a default judgment, you will only be able to go after your nieces assets in YOUR state. If she doesn't have any seizable assets, you will have to domesticate the judgment to her home state (PA) for enforcement.
Not a very rosy picture.. or much chance of recovery.
Finally, to your issue of why didn't the bank go after the niece first. Simple. They didn't have to. Your mother GUARANTEED repayment of the loan. As soon as your niece defaulted, the bank went after the guarantor. And they can't garnish wages without a judgment first. Why should the bank have to go to the expense and time of pursuing a deadbeat debtor when they already had a loan guarantor with the money??? Now it is up to you (and your mother) to try to recover your losses from your niece.