I would create a sql agent job with first 3 steps as the run of your three SSIS packages(i think the sp is sp_start_job) and chain them such that next is kicked off only if the first one succeeds.

Then have another step where you take data from all the three tables and update the required table. Now, depending on where your destination table is(same db or another server other db), you can do that in sp or as a seperate ssis.

Configure this step as the last step in your job. Again, this should be kicked off only if the first three steps have succeeded.

This will ensure that the you update / insert your destination table only once the three SSIS packages have been indeed succeeded.

Hope this helps.