How to ssh to a server using another server with key from the second server?

So basically you want server1 to act as your jumpbox, so you need one stanza for server1:

Host server1
Hostname server1.net
User server1-user-name
IdentityFile /path/to/.ssh/server-1-ssh-key

Then you need a stanza for server 2 that jumps through this one:

Host server2
Hostname 10.0.0.10
User server2-user-name
ForwardAgent yes
ProxyCommand ssh server1 nc %h %p 2> /dev/null
IdentityFile /home/server1-user-name/.ssh/server2-ssh-key