I doubt you’d want to reinstall a laptop while playing out. You could install all the necessary software on a backup laptop and just carry the relevant license keys with you in a text file. But … unless you had a fully up and running backup laptop with all licensed software AND you were using an external drive for your music AND you’d have all of your analysis files and database info on the external drive, you’d be very hard pressed to get all that in working order during a gig. So you’d need to make sure everything is synced between the two laptops before you start your gig to avoid problems.
Over on the main site there is an article about disaster recovery, it shows what I (as a mobile DJ) do when certain scenario’s occur.
Clearly if you are dependent on your gear continuing to function, then having a controller with stand-alone abilities and something with backup mix to hook up to it pays dividend. This will at least buy you some time to sort out what the problem is and to either fix it or to setup the backup.
Personally I find that a controller with an iPad and your core collection can be a solid backup that doesn’t break the bank or takes up too much extra space in your car.