With a credit score of 560-620 you might be able to "qualify" for a mortgage but it will not be a good mortgage product. Having less-than-perfect credit will limit the type of mortgage products that are available to you. Mortgage products do not even get exciting until your score is 749 or higher.
Why not work to improve your credit rating first, then qualify for a GOOD mortgage product, and then begin looking for your home? This way you set yourself up for success long term. A lot of people can get a home, keeping it? This is a core problem in today's market. I would like to see you and your family in a home with a monthly payment that make sense so you have have long term home ownership.
The Credit Repair Expert