  We introduce a new strategy to regulate the quantum entanglement in a
dispersive-hybrid system where a qubit is directly coupled to a cavity and a
resonator. A dramatic transition takes place by only tuning the squeezing
parameters associated with the vibrational mode. As the squeezing amplitude
becomes larger, the maximal entanglement abruptly falls to zero at specific
squeezing phases. It is also possible to generate entanglement for bipartitions
from the qubit-cavity-resonator system after applying this strategy. Entangled
qubit-cavity states are created through squeezing, even though there is no
direct interaction between them. We also analyze the effect of atomic, optical,
and vibrational losses on the quantum entanglement. Finally, we discuss future
realizations to implement all these ideas and promote further studies to
generalize the concept of monogamy in tripartite systems outside
qubit-composite states, in particular, $(2 \otimes 2 \otimes n)$-dimensional
systems.
