So I have decided to tackle the Battle Tree before SwSh gets here. I want to get to 100 wins in Doubles and at least to the 50 I need in Singles. Maybe, I'll try for the Multi as well, if I can.
My Doubles Team will be the one I beat all Maisons and Trees since XY, Aron/Dusclops/Mega Kanga/Conkeldurr.
However, since I'm trying to learn how to better play Singles 3x3, I'm in doubt of which team to use.
As you are aware, you'll definitely do fine with the Eppie special in Doubles.
As for singles, I have good news and bad news.
The good news is that if you are just trying to get to 50, just running a reasonable mix of Pokemon with a reasonable mix of attacks can get you there. So you should be able to make it.
The bad news is that your suggested team does have some notable weaknesses. First is Mixed-Mence. Draco Meteor is not a good option in the battle tree. That miss chance is just brutal, and can turn easy wins into losses. While in PVP battles, the "likely OHKO, small chance of a miss" moves are a great option, since the occasional loss to accuracy is worth the greater OHKO capability, whenever you are looking to put together a big streak of wins, you want to be minimizing variance. It also seems odd to go Mixed just for Crunch as your one physical-type attack, especially since it provides super-effective coverage against neither Steel-types, nor Faerie types, nor Blissey. Remember that because your STAB attacks are so powerful, a neutral Crunch is often going to be out-performed by a not-very effective STAB, and a Super effective Crunch will be outperformed by a neutral STAB. With coverage moves on big Dragons, you are thus usually looking for a potential 4x delta. Earthquake, for example, is 2x effective on Steel-types, where Outrage is 1/2x effective. Crunch doesn't provide a lot of these. Finally, you pay a very real EV price in going mixed. With just 92 Spa, your primary attacks lose a notable amount of pop. And even if you actually meant to flip your Spa and Att EVs, leaving you with 164 Spa, you are still losing a decent chunk of power just to support a marginal coverage move. I suspect you are better off going with a more traditional physical attacking Salamence, or even Dragonite, which can more easily steal a Dragon Dance or two thanks to Multiscale.
This takes us to Umbreon. Umbreon suffers from what I call "the Milotic problem": it's a reasonable Defensive Pokemon, but it can't take advantage of things it dominates. One of the best ways to win an easy victory is to have a foe that one of your Pokemon beats easily, switch in, set up, and then turn other future threats into cakewalks thanks to being set-up. Umbreon may be able to switch in and beat a decent number of foes, but then what? An unfavorable follow-up comes in, and you have no advantage going forward. This isn't to say that every Pokemon has to be able to set up. A couple of examples: Mega Metagross plays reasonably well on offensive teams with a Dragon-type lead as a weakness covering switch-in that can muscle through a lot of problems. Gliscor doesn't boost, and like Umbreon it can rack up plenty of KOs with Toxic, but Gliscor's big advantage is it is incredible at stalling out moves to allow its teammates to come in and set up freely. Umbreon is, in my mind, mostly a worse Gliscor, with its one advantage being that it doesn't stack a 4x ice-type weaknesses with Flying-type Dragons. (And even this can sometimes be an advantage for Gliscor to the extent that Gliscor can draw and stall out the ice-type move for Salamence).
And this comparison to Gliscor, and Umbreon's inability to either set-up or give its teammates a chance to set up leads us to a related problem: nothing on your team can set up at all. It's not just Umbreon who won't be at any advantage against subsequent Pokemon no matter how badly it dominates the lead; it's your whole team. If the opponent is reasonably bulky, can boost, and especially if it can Rest off Toxic, you may easily find yourself in trouble. Similarly, with no Substitute anywhere on the team, OHKO moves and status afflictions are a real threat. I'd feel much more comfortable if at least something on your squad was designed to set up, and you should consider a Substitute user as well.
All this said, 50 is a pretty modest goal, so extreme optimization is not required, and your team can probably make it. But recognize that it may take several tries for your team to get there, as your proposed squad has some big holes.