Mux mkv and dts file, change default audio stream and language
Based on this answer on stackoverflow, it seems that changing the disposition is now possible with ffmpeg (see also the official documentation).
I think that the command that you would need, so that the final file had English as the default audio stream is:
ffmpeg -i movie.mkv -i audio.dts -map 0:v:0 -map 1:a:0 -map 0:a:0 -c copy -disposition:a:0 default -disposition:a:1 0 movie_combined.mkv

The addition is -disposition:a:0 default -disposition:a:1 0. The numbering of the streams is for the output. -disposition:a:1 0 is needed to remove the disposition from the second stream.
(Instead of -disposition:a:1 0 you could also, in principle, use the non-documented -disposition:a:1 none, which has the same effect.)
To add metadata/language information, see the other answer.