As I've stated before in a thread earlier, game trainers are code-injectors. That's what they have in common with viruses. Anti-Virus programs like Malwarebytes do not see the difference between a hacktool virus and a game trainer.
I hope you have all your trainers in the same folder, because then you can exclude that folder from scans in the Malwarebytes exclusion list. Perhaps you should add it to your Windows Defender exclusion list as well.
I understand your reluctance to put your faith into 3rd party programs, but the reason you are here is because you want to use trainers to cheat in your game. I have moderate knowledge of cheat engine and code, and quite some experience using MrAntiFuns' trainers. You can trust this site and MrAntiFun released trainers.
EDIT: CheatHappens trainers are not that different from MrAntiFuns' trainers. They both inject/modify code for a specific named process. Perhaps your CheatHappens trainer was not built with Cheat Engine but with a custom program.