Gran doesn't accept no for an answer
You don't owe rude people politeness OP. Stop explaining yourself in an attempt to justify your parenting decisions. You don't need gran to agree/give permission/understand/be ok, with your ways etc. All she has to do is accept it. And she has absolutely no choice about that! You are DD parent, you make the decisions, not gran. If she keeps on at you, cease contact with her. Why would you visit, or be visited by, a bully? She'll see DD when your partner has contact time with DD, if he agrees to gran seeing her. It's nothing to do with you whether she sees DD or not, so remove yourself from that equation. You don't have to be bullied by this woman. You're justified in telling her to fuck off, literally.
I wouldn't say bored, it was him saying I'm not efficient enough, I don't stick to the routine and schedules on the dot and he's not understanding that it's hard to follow routines to a T with a young child
Efficient?! He isn't your boss OP. You're entitled to be as inefficient as you like. He's only on these shopping trips because he's financially controlling you. He could give you the money and you could go be inefficiently browsing the socks with flowers in and the stripey notebooks and the merits of these tomatoes over those ones, to your heart's content, if he doesn't like the way you shop. But he won't, will he, because then you're outside the home, even worse you're alone with just DD and worse than that, you're in a place where there's men - and he can't be having that now can he!
Him being trained in the army has drilled in this strict sense of routine and time management.
And him being an abusive arsehole is why he tries to force his ways onto you. He doesn't get to dictate what your routine is, how long it takes or even if there is a routine at all.
You. Can. Do. Whatever. You. Like. With. Your. Own. Life.
And if he doesn't like it, he can join his mother in far away fuck-off-land, the further the better really.