  In this paper we compute a presentation for the group of ring motions of the
split union of a Hopf link with Euclidean components and a Euclidean circle. A
key part of this work is the study of a short exact sequence of groups of ring
motions of general ring links in $\mathbb{R}^3$. This sequence allowed us to
build the main result from the previously known case of the ring group with one
component, which a particular case of the ring groups studied by Brendle and
Hatcher. This work is a first step towards the computation of a presentation
for groups of motions of H-trivial links with an arbitrary number of
components.
