  This paper considers two point boundary value problems for conservative
systems defined in multiple coordinate systems, and develops a flexible
a-posteriori framework for computer assisted existence proofs. Our framework is
applied to the study collision and near collision orbits in the circular
restricted three body problem. In this case the coordinate systems are the
standard rotating coordinates, and the two Levi-Civita coordinate systems
regularizing collisions with each of the massive primaries. The proposed
framework is used to prove the existence of a number of orbits which have long
been studied numerically in the celestial mechanics literature, but for which
there are no existing analytical proofs at the mass and energy values
considered here. These include transverse ejection/collisions from one primary
body to the other, Str\"{o}mgren's assymptotic periodic orbits (transverse
homoclinics for $L_{4,5}$), families of periodic orbits passing through
collision, and orbits connecting $L_4$ to ejection or collision.
