Thanks for your answers, I have been doing some tests to try to troubleshoot the problem.
The good thing is that it now works better for me but the bad thing is that I have no idea why!
To test the client mode I am using only one radio at the time in client mode and connecting my laptop connected via ethernet. Running a speedtest on the laptop shows me how much bandwidth I get on the client mode without any interferences to worry about.
I tested this with 3 different radios, the 2 internal radios from the pineapple and a TP-Link TL-WN722N USB dongle (which works perfectly out of the box on the pineapple). For the first couple of experiements I was getting very good bandwidth with the pinapple radio0 and the USB dongle (over 20-30Mbps) and very poor bandwidth with the pineapple radio1 (around 100kbps).
It looked like there was a problem with the pineapple radio1 so before reporting it I repeated the experiement in order to gather the exact numbers but that time it worked much better and I am now consistently getting around 10-12Mbps from radio1. I get less when I use radio0 as an access point instead of the ethernet port but it works, no more horrible pings.
To do these experiements I changed all the settings of the radios using the wifi manager infusion (which is very nice by the way). The only reson I can think of for the fix is that I have been shaking the settings of the radios back and forth...
At least if you have the same problem, I think it is a good idea to test the radios individually in order to eliminate as many variables as possible. I am now not able to reproduce the problem anymore.
I have not really investigated why radio1 gives me "only" 10-12Mbps where the other 2 radio can go over 30Mbps because 10Mbps is probably enough but that could be related to the original problem... I am not sure.