  We construct a smooth algebraic stack of tuples consisting of genus two nodal
curves, line bundles, and twisted fields. It leads to a desingularization of
the moduli of genus two stable maps to projective spaces. The construction is
based on systematical application of the theory of stacks with twisted fields
(STF), which has its prototype appeared in arXiv:1906.10527 and arXiv:1201.2427
and is fully developed in this article. The results of this article are the
second step of a series of works toward the resolutions of the moduli of stable
maps of higher genera.
