There are many more years of this ahead...so I recommend getting a buggy with a really good shopping basket underneath (a Maclaren for example is rubbish for shopping as it tips over when you remove and there is no proper basket, and you have hang things on the handles) There is bound to be one second hand that fits the bill. A lot of people have cars and don't need that kind of buggy, just want it to fold up easily. So that is first thing.
Second thing, is, I do get his point about picking things up daily. It is quite difficult to get everything for a whole week delivered including fresh food without feeling overstocked one half of the week and completely the wrong things left the other half (if you are me!). However, you can compromise on getting basics delivered, drinks, washing powder, pasta, detergent, potatoes, loo rolls, tinned tomatoes, oil, milk. If necessary just have it delivered fortnightly. Delivery is usually only £5 - surely it is not too much to ask that you pay £5 fortnightly?
Thirdly, if you try and settle baby for some of the naps and sleeps without rocking, it will help give you a break, even if initially it is hard work to change the pattern. If naps always take place when you are out and about try and use the sleepy time for you to have a break indoors, settling baby in cot, even if just for half an hour at the beginning so there is not always association with motion. When you are on maternity leave it may be cruel to expect baby suddenly to settle without you, when there is no-one to do the rocking and carrying..if baby is at a nursery there won't be anyone to do it, and no childminder will either.
Also, could you cook supper earlier in the day and reheat it? I am thinking lasagne (to do for two meals, freeze one batch) stew, chilli con carne with baked potatoes or rice, cauliflower cheese with ham and baked potatoes. All things that can be done v easily at last moment, no real cooking in the evening. It is a big change cooking dinner when you have had an exhausting day from the prechild days when cooking dinner was vaguely recreational. I literally did not have a repetoire that fitted my new life, it was all fancy pants pasta dishes, last minute sautes, freshly steamed veg, grilled goats cheese. Not good for life with small baby at all. Eventually baby will eat same food as you, so easier it is to have dinner the better.