I finally found out that as I have two VLANs with IDs 1 and 2, I had to change Default VLAN ID for trunk port not to be 1 (which is default). It has to be different from actual VLAN IDs passing through trunk port. I found about this by pure luck. I do not know if this is a bug or feature. I am noting it here in case someone else get into same problem, so he can find out in easy way.
If it is only a trunk port - only tagged traffic, then you are correct, the default VLAN ID should not be the same number as one of the actual VLANs. In my case for VLAN tagged only ports, I use 970 + port number as the default VLAN number - so port 1 is VLAN 971, port 2 is VLAN 972, etc. (note that I recently posted that I use 980 + port number in another post in error).
BTW, I highly recommend that you DO NOT use VLAN 1. Yes, it will work, but too many devices treat VLAN 1 different. In my case I use VLAN 100 for my cable based internet, and 101 - 106 for LANS that use the cable; and VLAN 200 for my fiber based internet, and 201 - 209 for LANs that use the fiber. Each VLAN has the VLAN number as the third octet of the IP addresses used on the LAN - so everything on VLAN 201 has 192.168.201.nnn addresses. Makes it easy for my brain to remember it...