improving soil with sand and rotovator

Is this the way to do it? I've dug up and either composted or otherwise thrown away the thatched grass covering about half the plot. The soil is a clay silt. Most of the weeds in this bit of soil are dead from previous mulchings. It's heavy to turn, especially with all this rain. The first 6 inches of soil are very dark, theres a lot of rotted organic matter there. Judging from nearby hydrangeas, which are very purple, i'd say the soil was alkaline.

Is the right way to go about improving the soil, to add sharp horticultural sand, and churn it all in with a rotovator? When dry, the soil bakes hard. Walking on it compacts it easily. I was thinking about getting one of those mantis tillers. Aren't there rules afoot that will outlaw 2-stroke engines?