Depending on your point of view, Captain Vye is either the world's best or the world's worst guardian. On the one hand, he lets his granddaughter do whatever she wants. If Eustacia wanted to throw a wild party, he'd probably just tell her to clean everything up in the morning. We see his laidback attitude toward parenting when Eustacia decides to temporarily join a theater troupe in order to stalk her dream boyfriend:
"Of course. But, Eustacia, you never did – ha! ha! Dammy, how 'twould have pleased me forty years ago! But remember, no more of it, my girl. You may walk on the heath night or day, as you choose, so that you don't bother me; but no figuring in breeches again." (2.7.9)
He makes fun of Eustacia in this scene and doesn't seem overly concerned about the trouble she might get herself into. Overall, Captain Vye seems content to live his own eccentric life and to let his granddaughter live hers.
But this attitude is also problematic. Eustacia really could have used guidance and supervision for much of the novel, and her grandfather's laissez-faire, or hands-off, attitude towards her leads to problems. Eustacia ends up marrying hastily, regretting it, leaving her husband, nearly committing suicide, and then running away and drowning, all while her grandfather basically pays her no attention. He only looks for her at the eleventh hour, on the night of her drowning, and we actually don't hear about him after Eustacia's death, which is rather telling. It's unclear as to how the loss of his granddaughter affected Captain Vye.
In the end, Captain Vye is a bit like Clym in that both do too little too late in their relationships.