You could fit this into one dropdown, with a 'Custom' choice at bottom. The user selects and gets a date range picker:
Since you don't have a lot of horizontal space in the design, you could show the range right below the dropdown, so they see the results of their choice right next to the 'Custom' label.
Here's another take with a bootstrap date range picker. You'll see they have canned ranges along the right, and calendars to the left:
In this model, you have the date span inside the input, rather than below (from my example sketch), and you have the calendar icon as a signifier as well.