I have small kids too. I built 4 3 card rigs and put them around the house. For the last 2 I used this small and light case: Fractal Design Core 2300 Black Compact ATX Midtower Computer Case and use only the fans that come with it, they are very quiet.
 
I remove the drive holder assembly and use the screw hole to hang one gpu vertically and connect with a riser, the other two cards are on the MB, the side cover just fits over the card that hangs. I use MSI Armor RX 580 8GB cards. the temps on one are:
74C
62C
73C

The other is:
73C
63C
71C

I have another with a bigger Fractal case with 3 MSI Gaming RX 580 8GB which has better temp:
64C
55C
58C
 
For comparison I have an open air 7 card rig in my office with MSI Armor RX 580 8GB cards and the temps are
58C
49C
58C
56C
59C
59C
60C