No, 4 days is (way) too short for tourists and especially in the winter.
Yes, you can probably drive around the ring road (Route 1) in Iceland; it's 1,332 km and the Golden Circle is only 300 km. The roads are paved, in good condition, and the maximum speed is 90 km/h (with a few exceptions in villages). That means that with ~5 hours driving per day, you should be able do to the trip, right?
First of all, you're at 64/65 degrees latitude. Mid-winter, that means only a few (3-4) hours of daylight, but you're going in late March, so that means 12 hours of daylight. Still, expect snowfall when you drive (you have no experience with that, so please rent a 4x4) and some parts of the road may be closed due to floods, excessive snowfall or mudslides. The Icelanders will try their best to keep the road open, to prevent villages from being isolated, but Icelandic weather can be very unpredictable and violent at times. Which means you're better off staying in a village for 1-2 days; you don't want to miss your plane because of that.
Even if you do manage it, you won't have time to enjoy all the sights and venues along the route (and there are many). I've traveled the Ring Road (without the Golden Circle) in 8 days a month ago (actually, two thirds of it, I went back via the F25, which is closed in winter); that was really enjoyable but it was during the summer. I have no experience myself in winter but I heard from locals (and read on the Internet) that one should plan at least 2 weeks for such a trip.
Regarding safety: Iceland, especially outside Reykjavik, is virtually devoid of criminals; I left my valuables in the car and even forgot to lock it sometimes. Cell phone reception is adequate along most of the Ring Road. It's absolutely safe, please enjoy Iceland with the three of you but do it at a slower pace :)