Airflow : dag run with execution_date = trigger_date = fixed_schedule

Take a quick look at my answer with start times and execution_date examples.

You want to run every Monday at 8am.

So this part is going to stay the same:

schedule_interval: '0 8 * * MON',

You want it to run it's first run on 2018-03-19, since the first run occurs at the end of the first full schedule period after the start date, you should change your start date to:

start_date: datetime(2018,03,12),

You will have to live with the fact that Airflow will name your DagRuns with the start of each period and pass in macros based on the execution_date set to the start of the interval period. Adjust your logic accordingly.

Your first run will start after 2018-03-19T08:00:00.0Z and the execution_date, every other macro that depends on it, and name of the DagRun will be 2018-03-12T08:00:00.0Z

So long as you understand what to expect from the execution_date and you don't try to base your time off of datetime.now() your DAGs will be able to be idempotent in operation. Feel free to make a new variable like my_execution_date = execution_date + datetime.timedelta(7) within any PythonOperator or custom operator (you get execution_date from the context of the task), use template statements like {{ (execution_date + macros.timedelta(7)).strftime('%Y%m%d') }} or {{ macros.ds_add(ds, 7) }}, or use the next_execution_date.

You can even add a dag level user_defined_macros like {'dt':lambda d: d+datetime.timedelta(days=7)} to enable {{ dt(execution_date) }}. And recently user_defined_filters were added like {'dt':lambda d: d+datetime.timedelta(days=7)} enabling {{ execution_date | dt }}. The next_ds and next_execution_date would be easier for your purposes.

While thinking about templating, you may as well read up on the built-in stuff out there: http://jinja.pocoo.org/docs/2.10/templates/#builtin-filters