Getting apt-get on an alpine container
Using multiple package systems is usually a very bad idea, for many reasons. Packages are likely to collide and break and you'll end up with much greater mess than you've started with.
See this excellent answer for more detail: Is there a pitfall of using multiple package managers?
A more feasible approach would be troubleshooting and resolving the issues you are having with apk. apk is designed for simplicity and speed, and should take very little getting used to. It is really an excellent package manager, IMO.
For a good tutorial, I warmly recommend the apk introduction page at the Alpine Wiki site:https://wiki.alpinelinux.org/wiki/Alpine_Linux_package_management
If you're determined not to use apk, and for the sake of experiment want try bringing up apt instead, as a first step, you'll have first to build apt from source: https://github.com/Debian/apt. Then, if it is produces a functional build (not likely since it's probably not compatible with musl libc), you'll have to wire it to some repositories, but Alpine repositories are only fit for apk, not apt. As you can see, this is not really feasible, and not the route you want to go to.