I've lived in Sheidow for nearly 2 and a half years now, and think it's a great area, imo. Same with Trott Park. There is an old and new side to both areas, and personally i prefer the new side. So if you're coming down from Lander Road, (from Hallett cove part) it'd be everything to the right. (first half sheidow, second half trott)
Also, think Woodend Primary is a great school. Had no problems there whatsoever and my child is thriving.
As Libby said there are some shops at Trott Park, which has probably improved a bit since Libby was there, as they have opened up a reasonably sized IGA Supermarket. There is a pizza/chip shop, doctors (I think from memory) and also a contours fitness place, not long opened.
As for swimming lessons, look in to state swim, there are several around adelaide. Most local to sheidow/trott would be Morphett Road, or Noarlunga Centre. There is also a swim centre in sherriffs road, (used it to begin with, but moved to stateswim as I wasn't that impressed) and there's also a blue dolphin swim centre, I think in Happy Valley.
Hope that's of some help.