Getting a mortgage with bad credit but a huge downpayment.?

I have a pretty poor credit score (long story with credit cards, personal loans and medical bills from age 18-22) I have had several car loans which I have never defaulted on and 4 years ago I purchased a house outright for 180,000. Since purchasing my house (3 bedroom) My husband and I have had 3 more children on top of our 1st child. A singleton and then a set of twins. Now we are obviously needing more room and have been searching our area for larger houses and getting ready to list ours for 180 and hoping to gross at least 165 when its all said and done. The houses in our area for the room we are needing are ranging for 230K-300K. Even with bad credit, if we have a 70% down payment, could we be considered for a mortgage? My husband is the only one working right now as I am in school finishing up my degree to become a DMS. We bring in about 3000 A month and once I start my career in the next 2-3 years I’ll be bringing in roughly 4500 a month ontop of his 3000. With our current bring in monthly and the huge deposit we would have, could we be potential candidates for a home loan?
Thank you for all of your answers. We really do not want a mortgage but houses around here that are big enough for our family are all pretty old and need a lot of repairs. We also considered getting another 3 bedroom that has a “bonus” room that is in our price range, but since we haven’t even listed our house yet who knows if that house will still be available when we do sell ours. The other house we were looking at is 220k BUT has been on the market for almost a year so we figured if we did sell our house before that one sold we could always offer quit a bit lower and hopefully have them meet in the middle. 165k is the least I would take but we could always get the mac we are asking since our house is brand new. Built in 2009 and we are original owners with all upgrades so technically if we sold for 180 and offered 200 and we accepted could we possibly be approved for a 20k loan? Again thank you for all of your responses =)

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