Et hoc dicimus Deum
What does it mean to "have a relationship with God"?
That depends on what "God" means, right?
Catholics often speak of "God" in an equivocal way. Sometimes, it's understood to refer exclusively to the First Person of the Trinity, sometimes to the whole Trinity -- and, I suspect quite frequently, it's not altogether clear in the mind of the speaker just how many Divine Persons are meant.
The thing is, Christians aren't called to have a relationship with "the whole Trinity," with "God" undifferentiated by Person. In a sense, we can't have such a relationship. We know by faith both that God is a Trinity of Persons, and that the Trinity isn't more, or other, than the Three Divine Persons. A Christian's "relationship with God" is a relationship with the Father, a relationship with the Son, and a relationship with the Holy Spirit.
Given the procession and union of the Divine Persons, each of these relationships is necessarily proportionate with the others. I can't truly love the Son and truly be lukewarm toward the Holy Spirit (though I can, of course, be convinced that such is the case). I can't love the Father and hate the Son, which is what Jesus tried to get the Jewish leaders of His day to understand. I can't love the Father as I ought to love Him if I don't even know the Son, which is one reason we should take Jesus' commandment to preach the Gospel to every living creature seriously.