Making the two interact (and argue) with each other will be key to completing the tasks in this area. The Back Gardens are clearly split into two sides, the Man's Garden and the Woman's Garden. Eventually, she'll take another way out and open the path to the next area. The garage door will close and the shopkeeper will be stuck inside. Once you're both inside, drop the item, then run up to the rope and pull it. How rude! grab something from the storefront and run into the now open garage, making sure to catch the Shopkeeper's attention. The Shopkeeper will open the garage door to get some chalk to make a No Geese sign. Completing this task will let you go to the next area. This task will unlock after completing some of the earlier tasks. Grab the radio last, as the Groundskeeper will chase after you, and if he notices the other picnic items, he'll start putting them back. The jam and thermos are on the table near the shed, and the radio will be moved to the same area after its initial usage to open the Garden gate. The pumpkin is heavy and difficult to move, so plan a distraction for the Groundskeeper to distract him while dragging it off. The carrot and pumpkin are in the garden. The picnic basket is right next to the bench, so drag it over as well. You'll need both sandwich halves to have the sandwich count towards the task completion. The sandwich and apple are on the bench when you first cross the lake into the area. This task involves taking a bunch of items around the Garden and placing them on the picnic blanket near the lake. Once you clear the garden entrance you should be home free! After the groundskeeper catches you, run back to the rake and drag it along the right side of the garden, so you don't get caught. Grab the tulip from the garden and start running to the left side of the garden. Go ahead and throw them in the lake, it's more fun that way. Do that, and you can quietly sneak behind him and grab them without him noticing.
The easiest way to do this is to move the cooler around so he has to pick it up with both hands. To do this, you need to grab the keys from the Groundskeeper's side while he's distracted. You can also complete this task by making the Groundskeeper wade in the lake nearby, which he'll do if he's trying to get an item that you threw in there back. You can make him come close by stealing and item and putting it next to the sprinkler. Turn on the hose when the groundskeeper is nearby and he'll get wet. Right on the outside of the garden is a hose connected to the sprinkler. The groundskeeper will come out and chase after you, opening the way. Grab the radio on the top of the bags of soil (move one of the bags out of the way) and it'll start playing.
The way to the garden is locked, but you can trick the groundskeeper into opening the way.