Round 1: Quite well, none of them would sacrifice the other since they've all shown to be a good team despite the arguments.
Round 2: Dealing with opposing teams and weird animals should be easy enough; Juugo went toe to toe with Yondaime Raikage and survived even two attacks from him. His Taren Fujizuho blasts away any fodder... He could use Kusari and Saibou Kyuin as a combo to take opponents organs from a distance etc... Suigetsu held his own against a Bijuu and survived a Bijuudama at point blank so he's no pushover either and Karin... she's smart, good at detecting potential ambushes, can heal and if she has Adamantine Attacking Chains, she can provide invaluable offensive support.
Round 3: (If there is one)... Juugo and Suigetsu are fine and if Karin has the chains, she'd be fine too.