FLR(o) immediate help please

Hi, I have a question about an FLR (o) application I am about to submit. I entered the UK in 2002, claimed asylum in 2002, was failed, and a appeal was again failed in 2003. I overstayed and did not voluntary return. I was never issued a deportation order. My wife a british citizen. We have supporting documents (tenancy agreements etc) to prove cohabitation since 2006. We married in 2010. We made a new submission in 2011 on the basis of our marriage. We were failed, the HO stating we had not produced evidence significantly different from the original asylum claim, and had not demonstrated any reason why we cannot have a relationship away from the UK. They did not dispute our relationship; it would of been hard for them to do with the extensive supporting documents we provided. I decided to apply for a judicial review on the basis that they failed to make a distinction between the original political asylum claim and our marriage. The HO did reconsider and basically bulked up their original reasons; that i can have a long distance relationship with modern forms of communication or we can both reside outside the UK. We have blessed with a child this year:-)
My main concern is that l have drink driving convictions between 2004 - 2007. I completed a drink drivers awareness course under probation in 2007, and have not re offended since. I never received custodial sentences, but did receive suspended sentences (below 12 months). I am now extremely worried i will pay the price of my stupid mistakes, and will have the application failed on the basis of being a persistent offender. Are driving convictions considered a 'serious enough' crime for them to fail my application and outweigh us being a family.
Any information concerning how the criminal offences might effect my application would be gratefully appreciated. Thank you