Replace the line if between two points

Using the strsplit method for @FrankieTheKneeMan:

x <- c("I like \\the big\\ red \\dog\\ $\\hat + \\bar$, here it is $\\bar{x}$",
       "I have $50 to \\spend\\",
       "$\\frac{4}{5}$ is nice",
       "$\\30\\ is nice too") 

# > cat(x, sep='\n')
# I like \the big\ red \dog\ $\hat + \bar$, here it is $\bar{x}$
# I have $50 to \spend\
# $\frac{4}{5}$ is nice
# $\30\ is nice too

# split into parts separated by '$'.
# Add a space at the end of every string to deal with '$'
#  at the end of the string (as
#      strsplit('a$', '$', fixed=T)
#  is just 'a' in R)
bits <- strsplit(paste(x, ''), '$', fixed=T)

# apply the regex to every second part (starting with the first)
# and always to the last bit (because of the ' ' we added)
out <- sapply(bits, function (x) {
                   idx <- unique(c(seq(1, length(x), by=2), length(x)))
                   x[idx] <- gsub('\\', '\"', x[idx], fixed=T)
                   # join back together
                   x <- paste(x, collapse='$')
                   # remove that last ' ' we added
                   substring(x, 1, nchar(x) - 1)
               }, USE.NAMES=F)

# > cat(out, sep='\n')
# I like "the big" red "dog" $\hat + \bar$, here it is $\bar{x}$
# I have $50 to "spend"
# $\frac{4}{5}$ is nice
# $"30" is nice too

This will always have cases in which it fails ( "I have $20. \\hi\\ Now I have $30"), so you have to keep that in mind and test it against other lines in the format you expect.