I, personally, have neither the resources, time, nor ability to make a framework like Angular. Unless (and arguably even if) you do, I really think you would be better off in even the short term spending the time you would be taking trying to make one on learning Angular (or React, if you prefer).
You would want to write a service that responds to HTTP requests to REST endpoints and interacts with that database. If you’re mentioning PHPMyAdmin, I guess that means you would probably select PHP for that task. On the client side, you would have to find or write a service that makes XMLHttpRequests to it. Well, that is, after you’ve written the event handling part of your framework.
I’m not sure what you mean by “normal” here, but if you’re already writing web apps in whatever manner you consider “normal”, and you’re basically asking if you can use Ionic as a glorified mobile-first sort of UI toolkit, the answer is still an emphatic “yes”, although I would still urge you strongly to rethink your opposition to using an established framework.