Installing teamviewer on Ubuntu 16.04 reproducibly breaks my monitor setup

TL;DR. My system has dual video cards (three monitors). This works great, but when I install teamviewer 12 the second card disappears. Why? How do I fix it?

My system has dual video cards:

$ lspci | grep VGA
01:05.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] RS880 [Radeon HD 4200]
02:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI] Cedar GL [FirePro 2270]

I have three monitors hooked up (two on RS880 integrated graphics, one on Cedar GL discrete graphics).

Here is what xrandr says:

$ xrandr
Screen 0: minimum 320 x 200, current 4240 x 1050, maximum 8192 x 8192
VGA-0 connected 1280x1024+0+0 (normal left inverted right x axis y axis) 376mm x 301mm
1280x1024 60.02 + 75.02*
1280x960 60.00
1152x864 75.00
1024x768 75.08 70.07 60.00
832x624 74.55
800x600 72.19 75.00 60.32 56.25
640x480 75.00 72.81 66.67 60.00
720x400 70.08
DVI-0 connected primary 1680x1050+1280+0 (normal left inverted right x axis y axis) 474mm x 296mm
1680x1050 59.88*+
1280x1024 75.02 60.02
1280x960 60.00
1152x864 75.00
1024x768 75.08 70.07 60.00
832x624 74.55
800x600 72.19 75.00 60.32 56.25
640x480 75.00 72.81 66.67 60.00
720x400 70.08
DisplayPort-1-0 disconnected
DisplayPort-1-1 disconnected
DVI-1-0 disconnected
DVI-1-1 connected 1280x1024+2960+0 376mm x 301mm
1280x1024 60.02*+
1152x864 75.00
1024x768 75.08 75.03 60.00
832x624 74.55
800x600 75.00 60.32
640x480 75.00 60.00
720x400 70.08
1280x1024 (0x48) 108.000MHz +HSync +VSync
h: width 1280 start 1328 end 1440 total 1688 skew 0 clock 63.98KHz
v: height 1024 start 1025 end 1028 total 1066 clock 60.02Hz
1152x864 (0x49) 108.000MHz +HSync +VSync
h: width 1152 start 1216 end 1344 total 1600 skew 0 clock 67.50KHz
v: height 864 start 865 end 868 total 900 clock 75.00Hz
1024x768 (0x4a) 78.800MHz +HSync +VSync
h: width 1024 start 1040 end 1136 total 1312 skew 0 clock 60.06KHz
v: height 768 start 769 end 772 total 800 clock 75.08Hz
1024x768 (0x4c) 65.000MHz -HSync -VSync
h: width 1024 start 1048 end 1184 total 1344 skew 0 clock 48.36KHz
v: height 768 start 771 end 777 total 806 clock 60.00Hz
832x624 (0x4d) 57.284MHz -HSync -VSync
h: width 832 start 864 end 928 total 1152 skew 0 clock 49.73KHz
v: height 624 start 625 end 628 total 667 clock 74.55Hz
800x600 (0x4e) 49.500MHz +HSync +VSync
h: width 800 start 816 end 896 total 1056 skew 0 clock 46.88KHz
v: height 600 start 601 end 604 total 625 clock 75.00Hz
800x600 (0x4f) 40.000MHz +HSync +VSync
h: width 800 start 840 end 968 total 1056 skew 0 clock 37.88KHz
v: height 600 start 601 end 605 total 628 clock 60.32Hz
640x480 (0x50) 31.500MHz -HSync -VSync
h: width 640 start 656 end 720 total 840 skew 0 clock 37.50KHz
v: height 480 start 481 end 484 total 500 clock 75.00Hz
640x480 (0x51) 25.200MHz -HSync -VSync
h: width 640 start 656 end 752 total 800 skew 0 clock 31.50KHz
v: height 480 start 490 end 492 total 525 clock 60.00Hz
720x400 (0x52) 28.320MHz -HSync +VSync
h: width 720 start 738 end 846 total 900 skew 0 clock 31.47KHz
v: height 400 start 412 end 414 total 449 clock 70.08Hz

My system is fully up to date:

$ sudo apt-get upgrade
Reading package lists... Done
Building dependency tree
Reading state information... Done
Calculating upgrade... Done
The following packages were automatically installed and are no longer required:
libasound2:i386 libexpat1:i386 libfontconfig1:i386 libfreetype6:i386 libice6:i386 libjpeg62:i386 libpng12-0:i386 libsm6:i386 libx11-6:i386 libxau6:i386 libxcb1:i386 libxdamage1:i386 libxdmcp6:i386
libxext6:i386 libxfixes3:i386 libxinerama1:i386 libxrandr2:i386 libxrender1:i386 libxtst6:i386
Use 'sudo apt autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

But when I install the teamviewer package:

$ sudo dpkg -i teamviewer_12.0.71510_i386.deb
Selecting previously unselected package teamviewer:i386.
(Reading database ... 213764 files and directories currently installed.)
Preparing to unpack teamviewer_12.0.71510_i386.deb ...
Unpacking teamviewer:i386 (12.0.71510) ...
Setting up teamviewer:i386 (12.0.71510) ...
Processing triggers for mime-support (3.59ubuntu1) ...
Processing triggers for hicolor-icon-theme (0.15-0ubuntu1) ...

And reboot...

My second video card completely disappears from xrandr and my third monitor stops working:

$ xrandr
Screen 0: minimum 320 x 200, current 2960 x 1050, maximum 8192 x 8192
VGA-0 connected 1280x1024+0+0 (normal left inverted right x axis y axis) 376mm x 301mm
1280x1024 60.02 + 75.02*
1280x960 60.00
1152x864 75.00
1024x768 75.08 70.07 60.00
832x624 74.55
800x600 72.19 75.00 60.32 56.25
640x480 75.00 72.81 66.67 60.00
720x400 70.08
DVI-0 connected primary 1680x1050+1280+0 (normal left inverted right x axis y axis) 474mm x 296mm
1680x1050 59.88*+
1280x1024 75.02 60.02
1280x960 60.00
1152x864 75.00
1024x768 75.08 70.07 60.00
832x624 74.55
800x600 72.19 75.00 60.32 56.25
640x480 75.00 72.81 66.67 60.00 

The monitor attached to it no longer works, instead it displays the 'kubuntu' boot logo forever.

A simple 'sudo apt-get remove teamviewer' and reboot later, and my system is fully functional again.

Does anyone know what might cause this? How do I fix it?