A.,
It sounds like you already have a lot of good advice, and "Yes" patience is learned (or more accurately - inpatience is learned). My girls are 10mos apart (not twins, so I get to go through the developmental stages back to back instead of together...) When the oldest was about your children's age we started the "temper tantrum free zone" which is anywhere I am. My girls get 3 warnings to stop the temper tantrum (for anything - the list is extensive and impressive <g>) or they can go sit somewhere "until you can pull yourself back together." I will then either get them what was promised, or they STILL won't get what was denied. "Move onto something else..." I got the idea from 1-2-3 Magic (forgot the author). The tears, repetitive requests, whining, etc. are harassment and should be treated as such. My one daughter used to throw a FIT if I picked her up from school(read day care) and didn't have her "milk." My husband came from home for them and would have a sippy of pediasure for one and milk for the other (my daughter was on high calorie too). I come to school from work to get them and do not have the requisite drinks. One day she screamed so much, that I counted her down, since I couldn't pull the drinks out of thin air. I pulled into a neighborhood on the way home, calmly parked the car, took her out of the car seat, and put her in time out on the side walk. There she sat for 2 full min (after she stopped crying) while I stood at the back of the car. We got home and she told Daddy we were late because she had time out. The girls are now 3 and 3 (almost 4) and understand "in a minute...not today...etc.,...oh, and 1-2-3."
Good luck. It will probably be worse when you first get REALLY firm with the limits, but like another mother said, "this is one battle you have to win." It's the only way to save your sanity AND theirs.
S.