How to make wifi and bluetooth work simultaneously?

This isn't an answer per se, as there is insufficient information provided in the question for me to provide a resolution, but a comment requesting this information would be difficult to follow.

Are you connecting to a wireless router on the 2.4 or 5 GHz bands? If you are typically using 2.4, does your router support dual band 'N'? If so, try configuring the router for 5 GHz, connecting to that, and seeing if the bluetooth behavior changes. The 2.4 GHz Wifi band and bluetooth spectrums have a great deal of overlap and can conflict with each other - this is an attempt to see if that is at play here.

If there is no change with that test, or you don't have a router that would allow you to try it, the next step is to collect more information on what is happening.

Please provide the output from the following commands. The dmesg commands should be run shortly after boot so that the relevant entries aren't rotated out.

sudo modinfo iwlwifi | grep -v 'alias'
sudo modinfo btintel
dmesg | grep iwlwifi
dmesg | grep -i blue
uname -a

Start the next steps in the 'working' configuration of wifi connected and bluetooth disabled.

1. Open three terminals as root and a fourth as a regular user.

2. In one root terminal run the command

btmon 

3. In the 2nd root terminal run the command

iwevent

4. In the 3rd root terminal run the command:

udevadm monitor

5. Finally, in the non-root terminal, run:

dmesg -w

6. Now with these monitoring tools running, try to simultaneously utilize wifi and bluetooth using more or less the same sequence of steps you described above.

1. Start with bluetooth disabled and wifi connected
2. Enable bluetooth
3. Presumably wifi will have disconnected; if so try scanning for a network so we can see what the logs report.
4. Try to connect to a bluetooth device
5. If connected to a bluetooth device, now try connecting to wifi again.
6. Disable bluetooth, and reconnect to wifi.

The output of these logs should allow us to debug what is happening here. You may want to obfuscate MAC addresses in the results, although please leave them uniquely identifiable.

Post the results on a website like pastebin, as some of them may be lengthy.