1) If the phone has a backup which isn't Too far back and hasn't backed up since, you could restore from backup. I'd check the backup settings and info under iCloud. It's unlikely but worth a shot, before you transfer the saves, if you're not interested in a little saved game surgery.
2) As far as I'm aware no mods on iPhone, and the only cheats available won't help you get bombs or an axe in the current situation. They're second only to Nintendo in their "You'll play our way or not at all!" attitude towards things.
3) If you don't have a backup and ARE interested in a little saved game surgery, here's how you can rescue this save:
In the saved game file (the bigger of the two), each "container" has an item listing for each item within it. For most containers (fridges and chests), it's just a sequential listing of items, however many are in there. For the player's inventory, because you can sort your items freely, there is also an entry for each empty inventory slot, which looks like this: <Item xsi:nil="true" />
So to get the Axe Out of the Chest, and Into her inventory, you would first search for it, to find the entry for it within whatever container entry it's stored in, and then remove it from there and replace an empty inventory slot with it. To make this easier to understand and follow along with, I decided to take some pictures. It should go without saying, but make sure you make a backup copy of your save before editing, in case something goes terribly awry. Here's my test farm, with the Axe in the inventory of a chest:
View attachment 8519
Now, to edit the save, I'm opening the larger file with Notepad. I right clicked on the file, chose "open with", and then from this list can choose "Notepad":
View attachment 8520
I then hit "edit", "find", and typed in "axe". I hit "find next" through all the pickaxe stuff until I got to here:
View attachment 8521
You'll notice about a third of the way down on the left you see that xsi:type="Chest" line, so we can see we're looking at the contents of one. We can see a </Item> flag immediately before the <Item xsi:type="Axe"> which we're looking at. The </Item> is Terminating, or ending, the item listing for the last item (in this case those mixed seeds, whose display name you can see on the line above). So we've got our start for the listing for the axe, we need to find the end, its own </Item> after all of its properties. In this case it's just to the left of that xsi:type="Object" for the bread on the next line. I can click the cursor right before the start of the flag for the axe, and then hold shift and click right after the end of its terminating flag, to get all the properties for the object, then right click and choose cut, like this:
View attachment 8522
Then, I can go back to the top of the save file, click somewhere on the top line, and use "edit", "find" again to search for a "<Item xsi:nil="true" />" flag to find an empty spot in my inventory. In this case I'm going to use the one right before the pickaxe, because why not.
View attachment 8523
I've highlighted it, and now I can just press "delete" to remove it, and then right click and "paste" the axe entry there.
View attachment 8524
I save my changes, load up my farm, and not only does it load without issue, in that empty space right before the pickaxe, we instead have our axe:
View attachment 8525
Going to the chest which held our axe, and opening it up, we can see it's perfectly fine. The next item over (the bread) and all subsequent items just shifted by one due to the absence of the axe:
View attachment 8526
Anyway that's a tutorial of how you would fix your save if it were a PC save. If you combine that with the link from imnvs, you should be able to fix this no problem. Biggest things to watch out for if you try this is make sure you don't mess up any formatting, move whole items, brackets (< and >) and all. If you mess up formatting accidentally or fail to remove the empty inventory slot you're replacing or otherwise totally mess up your save, it's not a big deal. Just make another copy from your backup (you did make a backup copy first right?) and then try again. If the file looks very different from what I showed, or if you're just terrified to try, you could also just attach the save to a post and I'm sure someone could lend a hand. I hope this helps, or at least was interesting!