Furanjaro wroteBut if I connect first Cisco VPN Client to my work network (default gateway), then connect with OpenVpn Gui to my VPN server (non redirect-/route-gateway), the DNS lookup looks like buggy
Probably, your work VPN is setting your DNS server to their own DNS provision where your personal server has no DNS record.
Ask your work Support for advise.
Or, if your home VPN server has a fixed IP address connect to it via ip address not DNS name.
Or, connect to your home vpn first.