PI to Ubiquiti and internet access

Paul,
I'm not sure I understand what your intent is.  When you say "my browser", are you referring to the browser on your RPI?  In my case, all I really wanted was my Raspberry Pi to be accessible from the mesh and advertise the services it had on it... which included an NTP server which in turn was synced to the Internet via the WiFi interface on the RPI.  That much was a simple case of doing as others have suggested here and disabling the default default gateway on the node.  You might need to reboot the node after changing that for it to take affect... I don't recall for sure. 

What making this change does is keeps the node's DHCP server from providing the RPI a default gateway IP at the same time it is providing an IP and DNS info.  Once you have made the change on the node and rebooted it, you may need to reboot your RPI in order for it to forget the old info it got from the node's DHCP server and get the new (which excludes the default gateway IP).

Why is this step important?  Because your WiFi interface likely is ALSO configured to use DHCP to get its IP... and it will get a default gateway as well.  So... if you don't change the mesh node's default behavior, your poor RPI is going to have TWO default gateways.  How is to know which to use?  Essentially, in that case if a destination address is on the net associated with the node it will send traffic to the node... and if is on the net associated with your WiFi network, it will send the traffic there.  But if the destination IP is on NEITHER of those nets... as is the case with public internet destinations... that is what "default" gateways are for.  But you have two.  Hmmm.  What is the RPI to do?

This is where "metrics" come in.  Each "route" (including default routes) that your RPI knows about will have a metric assigned to it by the operating system.  And it is different for an Ethernet interface (eth0) than a wireless interface (wlan0).  If memory serves, eth0 has the lowest metric number assigned by default and thus if you have two default routes, eth0 wins...IF... it is active (connected).  Thus... soon as you connect it to your node, your RPI tries to connect to the public internet through the node instead of through your wireless connection.  Not likely what you want.

The added complication comes if you want your mesh node to communicate to the public internet... VIA the RPI.  At this point, you must enable "routing" on your RPI so it will automatically pass traffic from one interface (eth0) to another (wlan0).  But... you also must tell it which traffic you want going where.  And that gets significantly more complicated.

If your only concern is the relatively rare situation where you want to update the node's firmware, I'd probably just follow the KISS principal and use your RPI's browser to download the relevant file and to manually upload it to the node.  If you also want to use Internet time... then just point your node at the RPI and let the RPI's NTP server provide the time.  It will essentially be Internet time since the RPI likely is already syncing its system clock to an Internet time source. 

And if you want your mesh to have access to the public internet via your node... then you'll have to have the relevant external switch so you can access your node's WAN VLAN as noted by an earlier poster.  In theory, I think you could do that via your RPI, but the routing and vlan configuration issues involved get you a longgg way past the KISS principal!

Hope my ramblings makes some kind of sense...

Dave