First things first, this question alludes to what is called the angular momentum problem. The problem is that while the Sun represents well over 99% of the mass of the solar system, it represents well less than 1% of the total angular momentum of the solar system. So what gives? I'll get back to this key point later.
Regarding the Sun: Our Sun is a middle-aged star. Young stars rotate quickly. Middle-aged stars such as our Sun rotate slowly. Old stars are even more sedentary with regard to rotation. The reason is that the stellar wind ejected by stars is a plasma (i.e., charged) and thus can and does interact with the star's magnetic field. This transfers angular momentum from the star to the stellar wind.
Regarding the Earth: The Earth, too, spun much faster when it was young, about one rotation every four to six hours. The Earth transfers angular momentum to the Moon's orbit. The initial rotation rate of the Earth had extremely little to do with the rotation of the protoplanetary disc from which the Earth formed. The initial rotation rate of a terrestrial planet depends almost entirely on the random geometry of the last few big things that smacked the planet during the final stages of the planet's formation.
Regarding star system formation: It is quite erroneous to invoke conservation of angular momentum with respect to star system formation. The formation of a star and the planets that surround it is a messy and rather inefficient affair. A one solar mass star system starts as a roughly 100 solar mass interstellar gas cloud. The 99% of the cloud that doesn't form a star or the planets that orbit the star is ejected, and this ejection can carry a lot of angular momentum with it. In fact, it has too, which leads back to the initial point.
Regarding the angular momentum problem: That our Sun accounts for less than one percent of the solar system's total angular momentum is but a small part of the angular momentum problem. A forming protostar must necessarily continuously shed angular momentum lest the protostar tear itself apart. A number of mechanisms have been proposed to address this problem. Two of them are rotating polar jets that transport angular momentum away from the forming protostar, and massive stellar winds that steal angular momentum from the forming protostar. There are others; this remains an area of debate.