  We estimate the distribution of relatively $r$-prime lattice points in number
fields $K$ with their components having a norm less than $x$. In the previous
paper we obtained uniform upper bounds as $K$ runs through all number fields
under assuming the Lindel\"of hypothesis. And we also showed unconditional
results for abelian extensions with a degree less than or equal to $6$. In this
paper we remove all assumption about number fields and improve uniform upper
bounds. Throughout this paper we consider estimates for distribution of ideals
of the ring of integer $\mathcal{O}_K$ and obtain uniform upper bounds. And
when $K$ runs through cubic extension fields we show better uniform upper
bounds than that under the Lindel\" of Hypothesis.
