As you've pointed out, the "problem" is the mixing of plants that need different watering schedules.
That said, it's still do-able, and not look like a hack job, but once you have things set up it will be difficult to change things. Here's what I mean... what you'll need to do to account for the watering schedules is to determine how much water the plants are going to need in a week, and compare that to your weekly watering schedule. Then you place the appropriate size and number of drip emmitters to get the desired amount of water to the plant during the time the lawn is watered. Of course if and when you ever change the schedule, the size/count of emmitters might need to change as well.
Otherwise, the key things you need to go to drip are a pressure regulator and a filter. One plan would be to tap into your existing line, run the tap to a valve box somewhere, then place the required regulator and filter in the valve box. Then run some more pipe from the valve box to a point above ground. The way I like to do that is run 1/2" copper from the valve box to the surface, and possibly up the sides of any pots... basically use copper anywere a week wacker is likely to ever be. Then terminate the copper with a copper female, and find a drip hose connector with a PIPE Threaded male like these (
http://www.lowes.com/pd_88290-1029-MLA-P2P_4294821977_44?productId=1103275) you can find at Lowe's. The thing to keep in mind is that the Drip Kits you see are usually designed to work with a garden house, and the threads on a garden hose and spickot are different that threads for pipe. As such, you would need to get filters and pressure regulators from an irrigation supply house rather than any sort of drip kit you'll find at a big box retail store. You need filters and regulators designed to go on pipe and pipe threaded connections, not garden hose threaded connections.