Easier to Harvest Garden in Skyrim Hearthfire
Solution 1:
You have to point your cursor directly over the surface of the object you are harvesting.
For example, if you are growing Mora Tapinella, then your cursor has to be directly over the mushroom itself in order to harvest it. Anywhere else (dirt, air, stump) and you will activate the planter dialogue.
Whatever you grow will stack over time, so one strategy to avoid meticulous harvesting is to just harvest less often. You will get just as many plants but it will be less of a headache.
Note: There is a bug with the creep cluster, where it is so low to the ground that it's practically impossible to harvest.