A councillor can take leave (e.g., medical leave) but that does not enable anyone to replace him/her.
There is no such thing as 'resigning temporarily' or 'temporary vacancy', even for a day. Either the office of councillor is vacant or it is not. If it is not vacant then the incumbent cannot be replaced, even for a day. The rules for dealing with a vacancy are set out in sections 204 to 208 of The City of Toronto Act. Council does not have the power to amend or ignore them or invent new ones.
If a councillor office becomes vacant more than 90 days before the next general election, Council must decide whether to fill it by a by-election (cost to taxpayers $225,000) or by appointing someone. If the office becomes vacant less than 90 days before the next general election Council can decide to do nothing.
Council's policy has long been that it will only fill a vacancy by appointment when a councillor office becomes vacant less than one year before the next general election, and otherwise it must be filled by a by-election.
Thus, given that the next general election is more than three years away, if Council sticks with its long-standing policy then Robbie would have to resign office so that Dougie could by elected in a by-election in Ward 2, then Dougie would have to resign office so that Robbie could be elected in a by-election in Ward 2. Two by-elections would cost the taxpayers $450,000 in total and, since a by-election seems to take about two months, the office would be vacant for about four months in total anyway.
Ford and Mammo no doubt will argue that the policy is based on the assumption that a replacement will most likely serve out the balance of the term of his/her predecessor and that it is not appropriate to use an appointment to fill an elected position with an unelected person for more than a year, but here all would be temporary: Robbie resigns, Dougie quickly appointed, then Dougie resigns, Robbie quickly appointed - and both are persons who have obtained large majorities from the electorate in Ward 2 to boot - plus, even if Robbie shuffles off this mortal coil the balance of his term could be served by someone who has demonstrated in the recent past that the good burghers of Ward 2 love him almost as blindly as they love Robbie.