Are there any Android apps that would track my location (at regular intervals, like every hour) and send coordinates directly to my server, without revealing this data to any third party?
There are some solutions available on the playstore. One of them is Traccar (the link belongs to the Android client), which logs to a traccar server you can define. The server software is open source (at least that's what the app description claims), so you can use it on your own server. Written in Java, it should run on most operating systems. For more details on this, you might want to check with the Traccar website.