I think a lot of the discussion, and both the OP and the DM in question, is missing what to me is the primary problem: the DM is not running the encounters well. He's not using the monsters' abilities to their utmost, he is not using good tactics, taking advantage of terrain, etc. And so he's not pushing the party.
That's really the core problem. Instead of addressing that problem, he's trying to address it by not scaling encounters down in order to make them tougher. And then since that would result in faster level gain leading to even less challenge, he scales back XP and loot. Then the OP, though he recognizes the issue with the way the DM is running encounters, sounds like his main frustration with the scaled back progress and whether the DM is following the rules for XP and so forth.
But the linchpin here is the encounters not being tough enough; everything else is simply downstream from that.
I'm not sure that I have any great advice about how to address that core problem, unfortunately. Running your own game and showing by example could help. Maybe trying to discuss with the DM after a game, in a nonconfrontational manner, how a specific encounter unfolded and what how he might have played things differently in order to make it more challenging. If he has trouble keeping track of all the numbers and gets overwhelmed with everything he has to keep a handle on, perhaps you could volunteer to be a bit of a DM's assistant - you could keep track of initiative and conditions at least, maybe monster HP. (Though if he's "old school" in the way that thinks it's heresy to reveal monster HP and so forth to the players, he might not be amenable, but you could still make the offer.)
But I think it's a pretty tough problem - if he's been DMing regularly for a year and hasn't gotten better, it might just not be something he's ever going to be able to do well.
There are a few side issues here as well. The DM does sound pretty stubborn, slightly adversarial, and not particularly inclined to respond to player feedback. That's not great, but it doesn't mean the game is necessarily doomed, or that you can't work something out. But it does make things more difficult.
Also, I wonder if there aren't other factors besides how he runs encounters that make the game seem less challenging. If the PCs are overmatched, but only slightly, they might be able to defeat encounters but at a higher resource cost than expected. How often are you taking extended rests? More and more often? If so, maybe the party is being "challenged" more than he realizes, in a non obvious way that could be brought to his attention. Are the rules for resting, limits on magic item use, etc. being enforced properly?
On the player's side: I wouldn't go so far as to accuse him of some unjust sense of "entitlement". Leveling up is fun; getting new loot is fun. If you feel like your rate of progress is being slowed, and not for some mutually agreed upon reason like "this is a low magic game", then that's frustrating! But again, I think that's not the real problem; the real problem is why the DM feels the need to slow progress. I humbly suggest to the OP that he try to shift his perspective to focus on that problem, and relax more about whether or not the "rules" for XP and loot are being followed. In the end, those rules are only guidelines, and the DM feeling the need to change them is a symptom, not the disease.
Finally, leaving aside that the other players are related or nearly related to the DM, it's important to ask: are they having fun? Is the OP the only one feeling frustrated? Other than these frustrations, is he enjoying the game? If so, again I humbly suggest that he try to alter his perspective and go with the flow a bit more. He may end up having more fun too. At least save his fire for times where it really will impact the fun of others - like for example, bringing in a new player two levels behind and keeping her there, which almost certainly would adversly impact her enjoyment.