I agree, with the mistrust and belligerence between the Wallies and Russia, and the Sec Council having veto power, they could only get involved in odd cases.
Perhaps the structure is changed so that the Sec Council doesn't require unanimous agreement (or non-dissent) for action but where the allowed involvement is spelled out and funding/participation requirements are related to approval. That is, if Russia votes against participation, they don't have to pay (much).
The other thing that's needed is a permanent force structure to serve as the framework for employing forces. Perhaps this is a small permanent staff, but every UN member also has to identify forces they'll use to participate in different tiers (small, medium, large) of conflict. Sending forces under a UN mandate offsets UN dues for a period of time.
Also, it might require that forces fulfilling a UN mandate actually operate under UN leadership (i.e. they wear UN berets and have UN commanders), though they could also coordinate 'coalition' forces (not under direct UN command).
The UN needs to have clear operating rules from the beginning, strong checks and balances, etc, so it's not seen as corrupt and incompetent.
Finally, it can't become a mobocracy where every country gets equal vote (regardless of contribution) and then just continues to tell the rich countries to pay. So, perhaps it's kind of a proportional representation thing, where each country's vote has a weight based on population, GDP, monetary and military contribution, and involvement in past efforts. This value could be tweaked every 5 years based on updates of data.
It's a forum for the great powers to talk before they decide to fight, doesn't work when the great powers don't agree. You need to avert a good deal of hostility and suspicion between the great powers where all of them feel as if they have global interests and responsibilities but yet not conflicting with one and another. Personally I would suggest some ill-defined and seemingly infinite threat that actually isn't a major power like the current war against terrorism :but in practice various Islamic-peoples.