First choose your software.
Since accurate beatgridding seems important to you, also on tracks that can be “off” your choices are limited to Serato and Rekordbox, whereas I find Serato a little more intuitive. Other options would include Cross or VDJ, but they have a steeper learning curve with those controllers and DVS.
Now that we have that out of the way I guess you will want to go Serato or Rekordbox.
They are both very close competitors and look really similar, so either will work for most people. I prefer Serato solely because of Flip and TonePlay which Rekordbox does not have, but those are more expert features.
Nevertheless from the controllers you then are into the Pioneer RX or SX2 which both have standalone mixer capabilities and also support DVS. Controllers you did not mention that also can do this are the Denon MCX8000 (which is what I use) the DDJ-SZ and those are the ones from the top of my hat.
None of those support iPads.
However if you daughter is just wanting to play around a bit, you can get something like an old DDJ-WeGo, reloop Beatpad etc. in the used market very cheap (100 bucks or less) and she can use djay on the ipad which is great fun.
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