Home office is always looking for an excuse to reject an application and if you admitted by giving them certificate, it is very possible that they might use that as an excuse. Hopefully there is no history of domestic violence. If you just had differences and then they were resolve then Home Office should not count that against you or your spouse.
Having or not having children is not heavily considered these days. Those days were gone when you had a child in UK, you will be given stay for the sake of child. That option was abused so they took it off the table. Now they say tat child has to live in UK for Seven years before they consider such applications.
It really depends on your documents that you have provided to Home Office. Most of the time, solicitor can explain things better then a layman. I strongly suggest that you consult an immigration solicitor before putting an application. Home office is making tougher standards of qualification day by day(This is just my opinion)
Good Luck