That old red stain will be a real bear to remove...I would leave it.
And I would try to re amalgamate the finish...I know there are some people who frequent these forums who say it can't be done....but believe me I have done it....and know a lot of tohers who have done it as well.
The trick is to find the solvent for the finish...most likely laquer thinner...but perhaps a mix of shellac and laquer thinner...2/3 shellac thinner and 1/3 laquer thinner....and then just brush that mixture on the old finish and re melt it together.
Of course try it on an out of the way spot on the chair....but on that old red finished stuff it most often does miraculous things to the old finish.
Linda C

wow - found a old rocker in dad's attic and similarly trying to remove old varnish along with torn wicker seat. The varnish coming off has left reddish,brown color- not on the enitre chair because of the different woods in its making, the color is wacky. I have done other old pieces but this one is a challenge. I will be trying different methods and will follow up, hopefully with good results.