In general, not for SSH specifically, I tend to close quoted bash strings instead of trying to figure out how many escapes I need. Especially useful for awk and sed.
I find it rather annoying to escape single quotes within single-quoted strings in the shell. Really, there are only two options, both of which are rather verbose:
$ echo 'A'\''A, B'"'"'B'
A'A, B'B
I suppose that there's a few different commands that would work for your example:
$ echo "One Two Three" | awk '{print "'"'"'"$2" here'"'"'"}' # original
$ echo "One Two Three" | awk {print\ \"\'\"\$2\"\ here\'\"}
$ echo "One Two Three" | awk '{print "'\''"$2" here'\''"}'
$ echo "One Two Three" | awk "{print \"'\"\$2\" here'\"}"
To be fair, though, the argument {print "'"$2" here'"} looks pretty weird if you're not used to working with awk.
In general, not for SSH specifically, I tend to close quoted bash strings instead of trying to figure out how many escapes I need. Especially useful for awk and sed.
For example:
Ok, maybe escapes would have been easier in this particular example. No wait, that doesn't work. Why didn't that work? ...Nevermind, my original way is still better for me.