I really think that claires arron is not the one who calls kate mummy. The timing is all off.
First of all, in season 3 ep6 -I do, kate does a pregnancy test which is positive. What happened to this baby???
After season 4 ep. Ji Yeon, this theory has really played on my mind. Sun has her baby in the 'real' world, which if Juliet is telling the truth means that Sun has to leave the island within the next three/four weeks(february) before her second trimester. Sun would then have her baby roughly junetime. Her and hurley seem as if they have been back in the real world along with the rest of the oceanic 6 for possibly a couple of months (the hospital staff knew she was one of the six).
So aaron would be taken off the island when he is roughly three/four months old. (claire was almost eight months pregnant when they crashed on sep.27 so aaron born the end of october).
Now when we see kates aaron at the end of season 4 ep -egg town, he must be roughly 2 years old. It just does not make sense that it would take say 18 months for kates trial to come to court. Considering that she was on her way to face trial when they crashed.It would not take them this long to reopen her case,apart from the fact that she should probably be in jail waiting for her trial, not in a lovely house setting up home with her 'son' for the last 18 months!
Another detail that bothers me, is the media coverage of the oceanic 6 was still very high at the time of the trial, I dont think that after 18 months on,the press would still be very interested in the oceanic 6.
Also jack seemed very 'together' at the trial, clean shaven etc. so it seems obvious that crazy jack happens way after this? So this would mean that it is at least 2 years before jack goes crazy and wants to go back to the island. Surely this cant be true! Something is way off!
So the only conclusion that i can come up with,is that kates aaron is notclaires aaron but her own biological son from before the crash! And just by coincidence has the same name as claires baby.

