While it is true that Doffy had the "best of both worlds" I think he had to build that back up to be able to reap noble benefits while still being a pirate. At the same time, despite being in that great position, he can still have a very real sting of being denied his birthright, because those are intense feelings he had as a child. Even though he's in a great position now, with everything he wants, that initial sting his dad put him through can still be very real. So for me it makes perfect sense for him to feel this way, to me Doffy seems like a real self made man, the kind of guy who had to build himself back up from greatness from basically nothing. That's what made him so appealing to me, and this falls in line with that.
The way I see it, Doffy definitely went through a number of stages growing up, he didn't start out always wanting to be a pirate or with his current personality, at least from what I figure.
So he grows up pampered as a noble, but since his father's a down to earth guy I think he had a childhood that was separate from the kind of life lived by Saint Charloss and etc, but still very affluent. I'm sure Doffy's father wouldn't go so far as to put on a mask to prevent his family from breathing the same air as the commoners, for instance. I'm sure they just enjoyed the privileges of being a noble like having slaves and a huge house. This makes sense too since Kid Doffy would focus on the actual perks of nobility which is why it would sting so bad for him when those were taken away. We can disconnect his birthright with the other nobles since he didn't exactly live like they did, he just lived as well as they did.
Then his dad makes all 4 of them trade everything away to live in basically squalor, in order to live like normal humans. His mom dies from shitty conditions, he gets pissed with what he's done to them, his mom, and not having what they had before. So he kills him, goes back to Marijoa expecting a warm welcome, but they still don't let him back in.
This is the point I think Doffy's character becomes what we know of him as today. That picture you posted above of him being happy and smoking, I think that represents a point in time after Doffy killed his father and learned that he was unable to go back to Marijoa. Doffy's hopes of returning to the life he loved (as a child, mind you, so his understanding of that life is already kind of biased and skewed) are dashed. So he "snaps", and realizes he's going to destroy everything those nobles stand for.
That's when he decides (probably with his brother) to go and become a great pirate, and from then on everything he does as he's pleased and is happy with everything. This backstory is a little jarring for Doffy based on the understanding that readers have built about his character, but at the same time it also gives more depth to his character. No one can be born like Doffy already happy and pleased with everything, having no regrets (except maybe Luffy). In this way we see what it took for Doffy to become the man we know him as today.
Doffy had always been pushed around, following the whims of others. Even though the intentions were good, he was pushed by his dad out of the life he loved and lost his mom. Then he tried to back, but the other nobles wouldn't accept him. So that's when he realizes he has to start doing what he wants instead of what others want for him and becomes a pirate and the it goes from there.