$50,000 In Debt...Advice Needed

Me and my wife have $50,000 in credit card debt. We also have a mortgage and 2 car payments. While probably not the best thought process I don't consider the mortgage/car payments as part of the debt I am looking to pay off because we need a house and 2 cars. Both cars have under $10,000 left to pay off. My salary is $80,000 (not including $3-$5K in potential bonuses) and my wife is a homemaker with no income. Our kids are 5 and 7 so this August she will go back to work part time as both kids will be in school full time...her income should be around $15,000. We have a plan that can get rid of 75% of our credit card debt in 1 year. First she would save every penny for 1 year when she goes back to work, lets say $12,000. We live off my salary now so we can definitely save 100% of her paychecks. Second we sell our house (owned for 7.5 years) for its current market value and after mortgage paid off and realtor fees we would have approximately $36,000. We believe we are eligible for a FHA mortgage which allows us to put only 3% down on a new house in the $175,000-200,000 range...which means we would have $30,000 left. If I take that $30,000 and add it to my wife's $12,000 after 1 year then we would pay off $42,000 of the $50,000 credit card debt after 1 year. After this we can easily pay off the last $8,000 in the next 3-6 months with our combined salaries. I am 40 and she is 38 so we are ok with starting over on a house mortgage if it means getting out of this mountain of credit card debt. Assuming we can sell our house and can get the FHA mortgage (3% down) on the new house...can anyone give any opinion/advice on if this is a good plan and maybe some other things to do or not do relating to our plan? Thank you in advance!