Well if your sources were correctly synchronized, your work would be extremely easy.

Get mkvtoolnix if you’re on Linux or Windows. It has different tools which allow you to work with mkv files, that includes different operations like muxing, demuxing and simple editing, and of course changing different things like attachments, chapters, tags etc.

However if you are sure the sources are not properly synchronized, your work will be much more complicated. It can be a framerate difference (e.g. your DVD is PAL, therefore 25fps and the Blu-ray is 23.976fps), in that case it would be pretty simple (just demux the audio stream from the DVD, convert the speed using any good audio editor (or besweet), and mux the corrected audio to the Blu-ray video.
If there is just a constant delay, you can do it directly in mkvtoolnix.
If the movies are a different cut (e.g. one of them is a director’s cut), you will need some video editor (and maybe before that use some software for converting the video to a format which you editor supports) but that shouldn’t be a problem, I think all 3 main systems have very simple and free video editors which will be capable of doing this.

Subtitles - it really depends on format of your subtitles inside of your mkv file. If it was created using some ripping software it will be as the graphic sup format. You can do some pretty basic operations on that directly inside mkvtoolnix, but for something complex you will need to first use an OCR to convert the graphical format to a text format (srt), and then edit the srt file to your needs - SubtitleEdit is a great free tool which does both.

If you want to go really fancy and want your mkv file to have things like cover art, named chapters, information about things like plot, actors etc. it can be done in mkvtoolnix using a couple of xml files