We present a unitary control pulse design method for a scalable quantum computer architecture based on electron spins in lateral quantum dots. We employ simultaneous control of spin interactions and derive the functional forms of spin Hamiltonian parameter pulses for a universal set of 1- and 2-qubit logic gates. This includes selective spin rotations with weak local g-factor variations in the presence of the global oscillating field and a Control-Phase operation with the simultaneous control of g-factors and exchange couplings. We outline how to generalize the control scheme to multiqubit gate operations and the case of constrained or imperfect control of the Hamiltonian parameters.