I’m in the same situation as you with a family running around the house most of the day. So I like to optimize too and have been trying to find the “best” solution for live improvised electronic music creation for a number of years. To be honest, I’ve not really found the DT / DN to be all that great for improv.
I would spend half my time programming a pattern so I can then drop mutes in and out and tweak a filter. I found myself questioning the whole improv aspect of what I was trying to do.
The most important thing you want to consider is going to be your sequencer. I’ve played many of them on this search for live play. The Elektron sequencers, while great, still require quite a bit of high level programming before you’re going to have anything useful.
I can recommend the NDLR, the Vector from 512, and (if you don’t mind software) the Ableton Push. The Push might be a stretch because of software and all that but given all of the max4live devices on offer you could really build yourself a live improvisational performance template that would blow anything else out of the water.
I have examples of various live performance rigs, from eurorack to the other devices mentioned above, on my YouTube channel. Here’s my most recent, using Push 2 and a max4live application called ACDGEN. Have a look at the video description for a detail of everything that is going on. It’s all live though, no clips or prepared midi even……