Don’t let yourself get upset because your son refuses to learn the alphabet. The alphabet, per se, is of absolutely no use to him right now. And it is something a child is expected to learn in kindergarten, not before. If you help your son acquire a good vocabulary, become able to sit and listen as a story is read, play and work by himself part of the time, be willing to share and take turns when playing with other children and carry on a conversation with another child or an adult, he will be far readier for kindergarten than he will be by simply knowing the alphabet.
Now, as for his and his sister’s behaviour in public, I think that is quite a different matter. Changing that scenario is probably going to take time, as my guess is that the two of them set one another off and that each one reinforces the other’s behaviour that you (and observers) don’t like. In that kind of situation, the disciplining parents have less power than they would like; no matter what you do, they are “rewarding” one another.
Probably your best bet is to strike a deal with them before you leave the house. And don’t hesitate to be completely honest. First, lay out a couple of cookies (or something they especially like). Then descote what happened on your last outing: “The last time I took you to the grocery store you embarrassed the heck out of me. If you act nice today, when we get home you each get a cookie.” Or, you might offer to buy something they especially like while you are out. But, if you do that, don’t give it to them until their trial period is over.
With that procedure you are offering a reward for their good behaviour. A variation on that is to withhold a reward if they do not behave properly. For example, if they act up, you can say when you get home, “I’m not taking you with me today because you both acted up last time.” (Don’t forget to repeat that when you actually do go out.)
Of course, the second arrangement requires that you have someone to leave them with when you go somewhere. The first technique is probably better because it keeps the reward closer to the behaviour you hope to change, whereas the latter one requires them to remember what they did at some time in the past and associate that with your current discipline. A final suggestion is to combine reward with distraction. I always had to take both my twins with me on my errands. In the grocery store, before beginning my shopping, I would buy each a box of animal crackers. Having them work through a box of those not-too-sweet cookies distracted them from one another and from what was on the shelves to give me just about enough time to do my shopping!
Finally, let me encourage you not to be too hard on them for misbehaving in public. We forget just how stimulating the places are that we take our children to. Just think of all the things they see on the grocery store shelves, many of which they want but cannot have. It takes time to handle that.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.