Well, firstly, play the war. I mean, presumably if they cared enough to start a war, they care enough to fight one. Werewolf on werewolf strategy can get bloody, creepy, and destructive to both the physical and spiritual fabric of an area.
The Pure get, by default, better deals with spirits than the Forsaken, so you can have the Pure make deals to have spirits screw over your party in innovative ways. Powerful spirits aren't something werewolves can just roll over. Also, think about the gifts and rituals that exist, the ones that have long term effects, and can be used by the Pure to attack your party.
Then, take a look at your list of antagonists, and try and construct something to throw them off. Looking at your descriptions of your PCs, it seems like there are a good few plot hooks right there:
- If your mobster has cast off his former life, you could have them not take that so well. Having to fight organised crime at the same time as the Pure, especially if they get together (Spirits of Organised Crime working against you -> funtimes), could be quite a nuisance. If they haven't, then their organised crime connections demanding that they get on with some casual work of a surprisingly difficult nature could be another way to go. (Werewolf Heist!)
- If your rich heiress doesn't dig the whole wolf thing, make the whole wolf thing not be terribly impressed with her either. Challenges of purity made by moon spirits, and having to fight for the right to gain new gifts, while trying to preserve their old life as much as possible, could work as a plot. Especially if you're running with that War on the Pure book where the Luna spirits actually come and give you free bonuses for your war, that could be something that engages their attention. Try to make them want to prove their worth, or else suffer.
- There are almost an infinite number of ways to use the possibly dead family. Have them turn up as enemy werewolves, balehounds, puppets of a maeljin, malevolent ghosts, normal ghosts with demands, possessed, even vampires or mages (though I wouldn't recommend mages, if they're interested in the werewolves I suspect they either steamroll them or get blended). Or they could turn up in a warehouse full of kidnapped, strung up soon-to-be Azlu.
- If you're not averse to splitting your party temporarily, having the Pure kidnap one or more of your PCs might be a good way to engage your protective biker's want to protect. With the pack mentality, breaking up a pack is a good way to disrupt their plans.
- For enemies within, not every party is up for this, but some people are: offer one of your players, in secret, the chance to become a balehound. Or, have an enemy start to corrupt their totem spirit, possibly by attempting to turn it into a magath.
In the best game of WTF I've played in, our GM basically had a policy of making sure we had at least 3 problems at any given time and only enough time to fix 2 of them. It worked pretty well, and meant that whatever we didn't fix ballooned horribly into terrible problems for everyone.
Oh, and one of the things about war in RPGs: if you take downtime to rest, that's time your enemies are carefully thinking of and enacting terrible ways to hurt you.