Police do not have to see you DRIVE. Circumstantial evidence can be enough to convict.
The case cannot be analyzed from YOUR description. The police report, video(s) and police testimony will likely fill in a lot of GAPS in this story.
Of all DIFFICULT cases for drunk driving, none exceed the difficulty factor for traying to get a Judge or jury to sympathize with any parent drinking, (much less drunk) with small children in the vehicle. (under ager 14 makes a NEW DUI case for each child in your vehicle.
Your lawyer likely has as good a deal as you will get.