Here is my problem. I do not want to have bitcoin-qt started every time I boot my computer and other computers on my local LAN. As It is using resources and also a lot of disk space on every computer.
You could just remove it from your autostart.
Here is my thought but I do not know if it is possible.
Could I setup a bitcoind on my server using docker and access it from my bitcoin-qt?
It will have the latest blockchain downloaded in one computer centrally and it will not take my desktop disk space and recources and it will also run all day.
Also as there are more than one computer here I could setup different bitcoin-qt for each user and save their wallet info in their computer but the huge blockchain folder is going to be in the server.
AFAIK this is not possible the way you are imagining.
But you could run your full node on the server and use SPV wallets on the clients to connect to it.
Either electrum together with an electrum server on your server, or simply using
Wasabi wallet on the client PC's and connecting them directly to your full node by editing the
Config.json.
The latter is probably the best option.
Also an other idea I had was to use a web based bitcoin client installed on the server. With that I could login from my mobile phone remotely via vpn and access my wallet securely without having to use any other web wallets
Definitely possible, but security risks always exist when something is accessible from the internet.
Only being accessible via a VPN does help, but shouldn't be considered absolutely secure. I would only use it for relatively small amounts.