[wereHamster]

You can not represent "Next Monday at 12:00" with a tuple (TAI, leap second count), because you don't know how many leap seconds there should be. Or maybe you know for next Monday, but you definitely don't know for the Monday in a year, as leap seconds are only announced ~6 months in advance.

[beering]

I think you cannot represent "Monday in a year at 12:00" with a simple integer either, right? For example, the king of the country may decide to cancel DST for the year. Either way you would have to store it as a calendar event and figure out the exact time once you're closer.

[dom0]

You should store that similar to this:

    begin = (today, 12:00) (eg. 2017-01-01T12:00:00)
    repeat = RRULE:FREQ=WEEKLY;COUNT=1;BYDAY=MO

Note that "begin" is usually something software figures out itself.