Regardless if it's the Old Hoe or the 50,000 Improved Hoe, Liana's Tool Bag won't accept it despite there being a "Hoeing" slot.

If you look at the item description of the toolbag, it tells you that you cannot add / remove items while the bag is equipped. You have to unequip it and then change the items, then equip it again. Also be aware that not all types of items can be put into the bag.

Thanks this was my issuse, an in game pop up message could help with this better I think. Not everyone reads the details of every item they are recieving and when you are new it's overwhelming with the amount of new things the game is giving you.