Minigame ideas:
Hammer Peril! (1v2)
Build an arena (10x10?) of holes for the players to be stuck in. The 1 player has the hammer and has to hit the other 2 a set amount of times before the timer goes off (Perhaps 10 times within 2 minutes? Or something). If you don't have a hammer, could use an axe?
Push-Of-War (FFA)
Surround a 5x5 patch with tiles. If you touch a tile, you lose. The goal is to push your opponents into the tiles so you're the last one standing. Time limit maybe 1 minute?
Shovel Mashers (Duel)
Both people have to mash their shovels against a rock. Whoever hits it the most within the time limit wins! No digging holes to help you against the knockback.
I was trying to think of things that would fit the Mario Party theme better. There are a lot of games that are 1v3 that give the 1 person an advantage over the other 3, such as a giant mech. Some of my favorite games were the 'battle' type of minigames, where you punch and kick each other off of a platform. And we don't have any duel games yet...