Install all mods on both (or all 3/all 9/all 42) computers. Assuming you're using a PC, your savegame file is in here:
C:\Users\LewZealand\AppData\Roaming\StardewValley\Saves
Obviously replace LewZealand with your username. You could try UrsulavonderLeyen but it might not work.
If you started your Farm in v1.5, then it will have your Farm name followed by a serial number. If you started in v1.4 or earlier, it will be your Character name followed by a serial number. That is your save file in it's entirety. It is portable and can be copied to another computer so you can continue to play your game there, even a Mac, though the save file goes in a different place.
I did this as I play on one computer during the week and another on the weekend, just keep track of the most recent update by looking at the timestamps of the enclosed files. And I've tested the portability from Mac to PC and back as I started playing SDV on a Mac and have moved that version of Farmer Bobbi (in my avatar on the left) to my PC.