$cat eval.sh
# The goal is to assign the value of $first to $1
# and the value of $second to $2.

first='$second'  second='boo far'

# 1)
# This first example exhibits the problem you are
# experiencing.  The quotes intended to delimit the
# string are taken as part of the string itself,
# since command substitution occurs after the parsing
# step which cares about quoting.

set -- `echo \"$first\" \"$second\"`
echo "First positional parameter: $1"
echo "Second positional parameter: $2"

# Outputs:
# First positional parameter: "$second"
# Second positional parameter: "boo

# -----------------------------------------

# 2)
# Adding eval passes the result from command substitution
# through the parser, and the quotes are indeed interpreted
# as you'd like.  However, with weak double quotes, if
# there is anything in the substituted text that would
# cause the shell to attempt parameter/command substitution,
# the output will be undesirably affected. In this case, the
# value of $first, the string "$second", is taken as a parameter
# which is then substituted, resulting in the value of $1 
# being identical to that of $2.

eval set -- `echo \"$first\" \"$second\"`
echo "First positional parameter: $1"
echo "Second positional parameter: $2"

# Outputs:
# First positional parameter: boo far
# Second positional parameter: boo far

# -----------------------------------------

# 3)
# The correct solution is wrap the command substituted values
# in strong quotes, to ensure that they are taken literally and
# not word split when passed through the parser a second time.

eval set -- `echo \'$first\' \'$second\'`
echo "First positional parameter: $1"
echo "Second positional parameter: $2"

# Finally, the correct output:
# First positional parameter: $second
# Second positional parameter: boo far