I would forget all about the alpha pack leader stuff that is spouted on the dog whisperer. He's a puppy. He's a male. Some hump, some do not. Some are easier to train than others. I don't really like the terms stubborn or defiant. Often a stubborn dog has just shut down because he is afraid to do whatever it is wrong, and has no idea what to do. I think defiant gives too many dogs way too much credit.
The pooping in the crate thing. House training goes a whole lot easier when we keep a solid schedule and empty out the dog. If a dog is running around like a nut in the morning instead of going poop, and you leave without the poop coming out, well it will come out. What I find works is to feed once or twice a day, and shortly after he scarfs up his food -- no free feeding, pick it up after 10 minutes, and do not give anything to the dog until the next scheduled feeding, within 3 days the dog should figure it out, that he either its now or never. After he has finished eating take him outside alone so he does not spend his time playing with another dog.
Do not play with him out there, if he comes to you, say, Go Poop. And wait until he has done the deed. Some dogs need to go twice, so you might have to stay longer. But do not engage him in anything. This is a potty moment.
Then crate him. At six months you may find that it is better to wait an hour or so after eating before he needs to eliminate. So long as he has already been out after waking up, that should be ok. If I leave a dog in a crate, then the last thing I do before leaving is a last trip outside.
If you start out with a schedule where the dog is relatively empty, you have the best opportunity of the crate remaining clean and comfortable, given the pup is not ill.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC