I think Drax does indeed have issues! Although he's learning to show some awkward humor and revels in battle, he's completely stoic when it comes to sadness. As shown in his interactions with Mantis, even while looking calm he is filled with sorrow at the murder of his family. I think this contributes to his loyalty to the team, adopting them as a new family and never wanting to leave a compatriot behind. His "father issues" are simply reversed. He is a father who has lost a child.