First, be very wary of real estate agents answering mortgage questions. FHA literally has NO CREDIT SCORE MINIMUM. Those that have stated there is an FHA 620 score are WRONG and should not be answering questions with bad information. Lenders, wishing their loans to be paid back, use credit scores as a measuring tool, it is the lender that imposes score minimums. I do not know of ANY lenders in this market willing to go below 560, and if they do a loan between 560 and 620, the borrower pays a much higher interest rate.
That being said, a 547 is, plain and simple, a terrible credit score and reflects a willful lack of discipline when handling your finances and terrible credit management. There are very few lenders that would take the risk on your loan, especially combined with "no big downpayment."
I would advise you to work on your credit and save for your downpayment. Once accomplished, you can apply and get a GREAT mortgage to buy you and your family a new home. There are many good loan officers that would help you formulate a strategy today to improve your scores over some period of time, then help you get a loan when your scores recover. During the process, as your scores improve, your LO can advise you of your mortgage options as they open up with your scores moving higher. When we help a potential client improve their scores, we do not charge for our services.
Good luck, Jim