The first problem:
Why should they wait 32 years to send the Sath? If the GTA/PVN is a high threat level, why not send in a whole lot more while they're still weakened by the first fleet's attack? Or better yet, if the GTA/PVN is now a high threat level, send in the beam equipped ships immediately, send in lots of newer capships, to pawn them as quickly as possible, then get on with the other conflict. Why wait 32 years to let the GTA/PVN (now GTVA) recover and develop beams themselves?
They simply didn't have a spare fleet in our sector during FS 1, so they decided to bomb the living s*** out of Vasuda Prime and Earth, and then just chase down survivors when the GTA and PVN would be falling apart due to lack of leadership.
Second:
It is implied that the Shivans nuked stars before Capella (during the Ancients). The Sathanes and the idea of star nuking was around for long before the GTVA. It was not a new creation.
@goes to FS wiki....
Though their empire was at one point extensive, they are believed to have been made extinct by a massive Shivan assault around 8,000 years prior to the events of Freespace 1 (i.e. circa 5,500 BC, note that this is also near the time the Crab Nebula would have been a supernova, hence leading to the question of whether the Shivans used their anti-stellar weapons on the Ancients).
It is not a proven fact that the Shivans nuked stars before FS 2, or that the Ancients lived in what became the Crab Nebula.
Also- I think the Shivans really just wanted to make Capella heavier through 'ghey subspace magic' in order to regenerate the nodes that the GTVA either collapsed or was preparing to, so they could continue pwning us on the other side. And here's their second epic failure, when the star colapsed and went Supernova.
Third:
Shivan Commander: Let's scare the GTVA by making a big jump node! They'll soil their pants!
Shivan Lieutenant: How will making a new jump node scare the GTVA? Why don't we use our shiny new @$$-kicking Saths to attack the GTVA?
Shivan Commander: Without the new nodes we're stuck, along with our shiny new @$$-kicking Saths here in Capella. Oh, and you're demoted.
Forth:
The Shivans not need plan do. Use Saths/retired Lucys/everything they've got. Why do they need a plan? They can kill us right now anyway. Making large tactical errors, like sending a small fleet to deal with a small threat which turns out to be a very big one, then doing some ghey fancy magic tricks, only for them to go wrong and lose half their Saths... This makes GTVA Command look like the wisest man in the universe.
Well nothing cannon implies that Command isn't wise

And since they assign threat levels to anyone they fight, it's because they need most of their fleet somewhere and they don't have resources to waste unless it's a real emergency. One more thing- what does a huge fleet give them when they can't move it to enemy space due to destroyed nodes?
Fifth:
The Lucifer did not fail entirely. Look what it did:
1) Destroyed a lot of ships
2) Destroyed Vasuda Prime
3) Destroyed yet more ships.
4) Got through all of GTA space to the very core, ONLY JUST failing. Two more minutes and Earth would've been a giant crop circle.
5) Collapsed the node anyway, effectively cutting off Earth.
Well since it was the first time in thousands of years when someone
survived their assault the destruction of Lucy WAS an entire failure, from the Shivan point of view:
1)they didn't kill us all
2)we killed them all, including their 'immune to primitive races' flagship
3)we actually weren't limited to hiding deep in a far away nebula and we were able to rebuild what they've destroyed (save 1 planet and 1 jump node)
4)who cares about a collapsed node when there are survivors on both sides?
The FS1 strategy failed only by the skin of the GTA's teeth. If the FS2 fleet tried the FS1's fleet tactics, the GTVA would be no more. Instead, the Sathanas fleet decided to do this:
1) Nuke themselves. 
Before the cataclysm, the Sathanes used to nuke stars and other large objects of immense gravitational mass to create artificial Supernodes to travel large distances.
I actually use a very similar idea, but to recreate the normal nodes the GTVA was destroying.
But this time, after hundreds of succesful star nukings (I think that there were countless civilisations that tried to block off the Shivans, so they developed node-recreation technology), they made a supernova. And that's why only some ships warped out- the others simply didn't notice something went wrong untill it was too late.
If the Shivans could wipe out the GTVA just with sheer brute strength immediately, why wait?
Maybe because the Sath fleet had to come from some very remote place (they can be seen in transit in the 'DIVE DIVE DIVE' mission)?