At the risk of appearing to be cold-hearted, I will still ask questions that you need to ask yourself, and to answer honestly: can you really afford this property? will you lose equity in the property if you lose the house, or is it "upside down" on the mortgage, meaning it is worth less than the amount owed? can you find a place to rent in the same area for less money?
This may not be legal advise but instead a discussion as to whether you should fight so hard to keep the property. Most attorneys who handle foreclosure matters know that their clients are not bad people, or people who seek to scam. So this is not a morality discussion. It is a practicality discussion. I realize from your question that you have paid what you could, but have fallen way behind.
First, to answer your first, question, the answer is "no", there is no basis in law to force the bank to accept reinstatement in partial payments. You can ask, and if the bank would consent, that would be wonderful. But they have no requirement to do so.
What should you do? Be honest with yourself. How in the world will you be able to pay the 2nd half of the $9k reinstatement? How will you obtain the money? Your minimum-wage job probably willl not be enough to put food on the table or gas in the car and insure it, much less enable you to save $4,500.00. And in the meantime, while you are putting the second half of the money together for the 2nd payment, you are falling behind on your new monthly payments.
There are programs to consider, one of which is Florida's Hardest Hit which will pay the reinstatement for you, but the process is complicated. You should contact local churches, the Legal Aid Society, call 211, Urban League, or similar entities for a referral to an attorney or a group that will assist you in your applications.
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You are free to ATTEMPT to negotiate a deal that either settles your debt or settles the foreclosure/default. However, your mortgage probably allows the bank to proceed against you at this point unless you pay the mortgage in full through something called an acceleration clause. As a legal matter, you are not out of the woods with regard to the foreclosure action unless you completely pay off the mortgage or come to an agreement with the bank to dismiss with foreclosure proceeding in exchange for some payment or payment plan.
The information provided in this and other answers on Avvo are general in nature and limited to the facts as stated. The information provided in this and other answers on Avvo should not be construed as legal advice on which the reader relies without further consultation with an attorney. No attorney-client relationship is created on Avvo question & answer forums. This attorney is licensed and admitted to practice law in the State of Florida only.
Excellent advice from Ms. Schofield and Mr. Lampert. You can ask to split the reinstatement quote into two parts, but your bank is under no obligation to do so.
The bigger question raised by Mr. Lampert is whether you can afford this house, and you need to be very honest with yourself in answering this question. Even if you catch up now what about the future? Even with all of the extra hours that you work it seems as if you are paying a much higher percentage of your income than you should be on your home. Perhaps you can speak with a local foreclosure attorney about all of your options. A short sale (assuming you are upside down), along with your tax refund, might leave you with enough money to make a fresh start with a lower payment somewhere else. Good luck.
As Mr. Schofield said, your loan is "accelerated," meaning the entire balance is due and payable immediately. As a result the bank doesn't have to work with you or accept your terms. As another poster commented, the real question is what is the value in this home and is it worth saving? If there is equity and you can afford monthly payments on a "go-forward" basis, then don't waste your time re-negotiating with the bank; beg, borrow or steal to get the money to lock them into the deal they already sent you a letter that they are agreeing to and make it happen. If not, then look at your best strategy to walk away with minimal exposure.