You think Crocodile's gonna blow his stack when he finds out how shitty Luffy's upbringing was? His baby boy repeatedly got tossed into the jungle to fend for himself against wild animals, as well as off cliffs and left to float into the fucking air on balloons all courtesy of Garp. He got left alone for long periods of time possibly as early as infancy, also cuz of Garp. And oh yeah, he was tortured by pirates, almost burned to death in a giant garbage fire, and went through the trauma of losing a brother.

Like, no matter how stern or distant of a parent Crocodile may be, I don't think he would be content to stand by and let any of that happen to baby Luffy. Also also, Crocodile witnessed firsthand Garp impeding Luffy's attempts to rescue Ace. The Cross Guild wants Garp for his bounty. Crocodile wants Garp for REVENGE.

With Garp I feel like it could go either way because like, let's be real for a second

This is 100% played for laughs.

Like if we're being serious then yes, in the Very Real World this is absolutely child neglect and abuse, Garp's parenting would NEVER fly (🥁) in our Very Real World. But just like Nami can physically abuse Luffy and co for laughts and get away with it, Garp's "training" is very much the same tonally, a Cartoon Slapstick Gag (made even more obvious when Toei animated Baby Luffy flying off into the sky going "UGYAAAAA" (that clip lives in my head rent free it's so funny??)) and a reflection of how this ridiculous old man (who might've been through even more ridiculous training in his childhood) views how a small child can be trained.

And so like. I could imagine Crocodile being like "who the fuck does that to a small child, are you insane" at Garp if he found out how Garp had been raising Luffy, but I think whatever reaction Crocodile might have would be played just as much for laughs as Garp's original comments were

Like IDK if Crocodile and Garp did have a relationship I think it would end up being similar to how Zoro and Sanji interact. Like Crocodile would to some degree be indebted to Garp because Garp did look after his son when he couldn't, and Garp wouldn't have a precious grandson (whom Garp sincerely does love, deeply) without Crocodile, so like. I think there could be like this mutual respect and gratitude for the other. But also it'd be kind of a begrudging gratitude and they would also hate each others guts and what they stand for and probably bicker. Lots. But in a funny way. (Like Zoro and Sanji)

Also I feel like even if Crocodile personally hated Garp's guts I don't think Crocodile would ever try anything to harm Garp. Like he saw how Luffy absolutely shattered after losing Ace, so even if Luffy and Garp's relationship wasn't the strongest, if Luffy loves his grandpappy then I don't think Crocodile would want to take his son's only grandfather, his family, away. Crocodile isn't in any kind of position to "take revenge" on the man who did look after his son for him (even if his methods were questionable at times) (Same for Dadan and the bandits too arguably)

The convenient thing of me letting this ask sit in my ask box for 20 days before actually responding is that I managed to post this thing the other day, and I want to continue an observation from that post; While I do agree Crocodile would probably be horrified to find out about all shit Luffy went through as a child... In the end, what's happened has happened, and I think Crocodile might believe that if he had wanted to ensure his son wouldn't have to go through things like that, then he should've raised the child himself. That Luffy's childhood not being all sunshine and rainbows is kind of his fault.