Try this and tell me if it worked for you, because I'm not having any problems on my end.
1. Launch Trainer in Administrator Mode
2. Launch Game
3. It should prompt you whether or not you'd like to run:
A. Play 7 Days to Die
B. Launch Game Without AntiCheat
C. Show Game Launcher
(I launch the game from Steam. Running Alpha 14.7, legitimate copy)
4. Choose "Launch Without AntiCheat"
5. After the game has started up, load up a game you created.
6. When the game is done loading and you're able to play, Press F1 to activate the trainer
7. Alt+Tab to the trainer and see if it activated
8. Repeat steps 6 and 7 a couple times until it activates. (If you hover your mouse over the trainer you can see it loading because it takes a second to inject the program)
9. After the trainer has been activated and you've activated a couple of the options, you should be able to use the trainer without having to Alt+Tab. You should be able to press the buttons while in-game without an issue.
It's just like jiggling keys in a lock to get it to turn right. Sometimes you have to fiddle with things to get them moving. If this doesn't work for you or you get stuck or confused just say so and I'll try to help you get through it.
Also, It's important that you select the "Launch Game Without AntiCheat" option otherwise it could blacklist you from a large multitude of servers. There's a way for admins to see whose been banned by EAC(Easy Anti Cheat) and blacklist you from joining their servers automatically.
I don't know if this works online with other players, if it affects other players, or if it is easily detectable on servers other than the one you host. I'm not going to test it either. If you cheat on a multiplayer server and get banned it's your own fault.