For the most part, the built in wifi on the CQ becomes its own little wifi network between itself and client devices controlling it (with CQMixpad and CQ4You). Essentially this is a dead headed network without access to the outside world. Now, you could join the computer (running the DAW) to the same CQ network and you may be able to do both at once (but will not have internet access). I haven’t tried client to client communication when joined to the CQ wifi net so not sure if it works.
I’ll tell you, I was originally excited about the onboard wifi in the CQ but the way the networking stack was implemented was pretty limited and single focused. I’ve moved away from onboard wifi. For $40 you can get something like the GL-iNet Opal travel router and you will have much more flexibility. If you travel with this then the CQ connects to it using the wired port. Your clients can connect wired or wirelessly to the CQ, via the Opal, without having to reconfigure network settings in the CQ. This is handy because you cannot do simultaneous wifi and wired network access with the built in CQ networking. Also, you can use the router functionality of the Opal to connect these wired/wireless networks to the Internet or upstream networks. The Opal supports wifi repeater mode for the WAN side so, if you’re in a venue that has its own wifi guest network, you can simply join the Opal to it and all your clients (including CQ and controlling devices) get access to the Internet (if that’s needed/desired for a given setup).
Bottom line is that, if you’re doing wifi control of two different things on your tablet then both of those things need to be on the same network (likely) to work. Creating your own little live-sound network with something like the Opal will likely give you lots of flexibility going forward.