You were always exempt from the provision that made it unlawful to be in possession of a firearm while intoxicated (571.030.1.(5) ), if you were engaged in a lawful act of self defense. That hasn't changed.
As to the original question:
I can carry a weapon in an establishment that serves alcohol, if I have permission from the owner
That is correct. In fact, it isn't unlawful to carry in the establishment even without permission from the owner.
.....Now if that is the case, can I be arrested for drinking and carrying a weapon as long as I am in the establishment?
No, not necessarily. It was never unlawful to be drinking and in possession of a firearm, regardless of where you were. It was only unlawful to be "intoxicated" (as defined in RSMO 571.010.(11) ) and in possession. The act of drinking an alcoholic beverage, in and of itself, NEVER satisfied the definition of "intoxicated".
Just a thought, but if this is PRIVATE property....would the "intoxication with a weapon" have any merit?
Prior to August 28, 2010, yes, it would have had merit. In fact, it is because of an incident that took place on private property that this law was changed. It was, quite simply, unlawful to be in possession of a firearm while intoxicated unless you were engaged in a lawful act of self defense, regardless of where you happened to be at the time.
OK..I know I would be busted the minute I left the place, ( unless I left my weapon inside) but if the owner allows me there, he also has the right to tell the cops to get out and not harass me...
Actually, that is not the way it worked. The statute made no distinction as to there being any exemption if you were on private property. If an officer had reasonable belief that you were in a "substantially impaired mental or physical state due to the introduction of any substance into your body", you could be charged under RSMO 571.030.1.(5), which was a Felony charge. That said, an officer would have to have RAS to enter YOUR private property before he or she could make contact with you and evaluate your "intoxicated" state, but he or she WOULDN'T need RAS to enter a publicly accessible place such as a bar at which time he or she could casually observe your "intoxicated" state, which, combined with the presence of your firearm, would have been unlawful under the prior language in the statute.
As has already been pointed out above, as of August 28, 2010, RSMO 571.030.1.(5) was amended. It is no longer unlawful to simply be in possession of a firearm while intoxicated. In addition to being intoxicated and in possession of the firearm, you must now also either discharge it or use it in a negligent or unlawful manner, before it is a crime.