I've always shopped on my own with one, two or three kids (in various combinations) over the years and yes, no matter how you do it, it can be a real PITA mission.
I have to travel an hour each way (live in the bush) and it has to be done during the week, so I tend to do it fortnightly on a Thursday.
The key I think is to have a detailed menu plan and list and know your shop well, so you are in and out as quickly and efficiently as possible! Distract and entertain kids of various ages with their own baskets, or get them to put things in the trolley etc.. have water and snacks etc... My older ones know that if they put on a performance whilst shopping, their will be unpleasant consequences.
I don't know where you live but if you have a few different supermarkets/locations to choose from, could you split your big shop over two mornings per week after a morning outing? Then get home and they have their arvo sleep while you unpack groceries?