Re-reading the original post, there seems to be multiple problems here that cannot be diagnosed without being there. Your A/C of course is designed to come on and off based on your inside temperature, so the outside temperature, time of day or night, etc., would have nothing to do with it's operation. Any normal, currently running A/C unit should maintain the temperature you are seeking.
Since the home is less than one year old, it should be under warranty. For homes no longer under warranty I often recommend Chuck Ferrall...I have never met him, but he has many positive reviews here. In this case, this being a new house, it seems that the homeowner should not have to pay for anything....he just needs someone out there with the skill set to troubleshoot and remedy the issue.
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Florida licensed Home Inspector #HI688. (352) 250-7818
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