I am not sure I understand your term 'two independent vlans'. Do you mean that these vlans are local to that switch only?
When configuring multiple vlans on the Cisco and small business switches, you need to configure trunking inbetween the switches IF YOU WANT the vlans to span the multiple switches.
Trunking will ensure that non native vlans (by default vlan 1) will have a the correct 802.1q / vlan tag on it; this is called vlan tagging or frame tagging.
The small business switches can be a bit confusing in that you have to make sure the vlans are marked as tagged and not excluded. On some models, by default these additional vlans are set to excluded, meaning that these vlans cannot traverse a trunk / inter-switch link.
If you want these vlans to span multiple switches, then make sure to check your trunk configs and ensure that all vlans are set to tag - except the default or native vlan.
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