You could do a pickup order, and then they load it in the trunk, and then only take the groceries inside with you. Then, when the kids are asleep, go out and bring the presents inside to hide.
This is when Amazon or delivery is awesome! Side note, my 5 year old found our Christmas presents before I could wrap them... from Santa, so she got to type a letter..... Also, you can have your SO go to the store and send you pics after work. Another thing we do too.
Oh fellow mom, don't feel guilty. We all have so much on our plates. I also haven't gotten my kids christmas gift, plus I will need a few extra for my older son has a birthday 9 days after Christmas. I also can't take hom with me shopping and it's a bit of a hassle trying to carry or push a stroller around with a 6week old.