When will we send a remote controlled machine to dig into the mountains of Mars so we can eventually have a sealed large cave to work out of?

You have got the right Idea
 There are Lava Tubes around the Giant Extinct Volanoes

 WHEN  as in date time   I have no ability to KNOW  as to "WE" that is not a collective of  human populations ..... actually  a quest of different  GROUPS  of PEOPLE   ORGANIZATIONS  and independent COMPANIES  are  exploring the technology for such adventures .  


  they do not  SHARE that with "ME" as an individual  i am not  a scientist or a group or business member   but  occasionally  such members announce to the PUBLIC their advancements  and plans


... as  CAPTAIN KIRK  says to GO where NO MAN has gone before  the PEOPLE with the MONEY   to EXPLORE  such technology   generally do it with the GOAL  , purpose MOTIVATION of a ECONOMIC RETURN  aka MORE MONEY MINING for gold  minerals  fuels  or something of VALUE  in CONTRAST to generally speaking   " SCIENTIST " for the  "KNOWLEDGE " and information  about the universe


 thank you for the inquiry

We do not NEED to dig tunnels into mountains. Mars already had lava tubes. Yes, the do need to be made air tight and have AIF licks put in, but the ti Nels ate ALREADY THERE in Mars AND. the Moon. It is ignorance like yours that is holding us back. and your ignorance is very contagious and is now pandemic be a use it goes viral so rapidly.

No, because there's no chance people will ever go to Mars. It's technically feasible to get there but the political will to do so isn't available.

work out of and do what ... we cant even solve common social issues here ...

What would we actually do there?

There's plenty o suitable places rigt here on Earth if anyone hankered to live in a hole in a bleak rock strewn desert.

Digging a cave would be very hard to do. And rock is not airtight. And it would be hard to deal the opening.
It would be better to just take a habitat made of plastic or glass or metal and set it up on Mars.