協力しよう、という提案を無碍{むげ}には断れなくなってしまうのだが
Can someone help me make sense of this?
協力しよう=let's cooperate
という提案を=This proposal
無碍には=Without any obstacle
断れなくなってしまう=End up becoming unable to refuse
の=Nominalizer
だ=copula
が=But
Let's cooperate. Without any obstacle I ended up becoming unable to refuse this proposal, but...
I think this is how it should be translated, but I am still not sure.