Let's say for the sake of arguement that Operation Doppelganger fails. Hanse will definitely want payback, but without the Lyrans to pin down a large level of the DCMS's forces he can't really afford to work on the same scale, at least for long.
And with the Third Succession War still being fought, there's a slow drain on his resources that will make it harder to maintain a sustained offensive. Still, he can probably pull a largescale operation like Operation Rat off if he has to, he just can't keep it up as long.
There's no reason I can see that the lack of a Federated Commonwealth would prevent the Dragoons and Dragon from falling out, and with Takashi having something to fixate upon, I could see Hanse relying on the Dragoons (with more reinforcements than in canon) to keep the DCMS busy while he tears into the Capellan Confederation. He has Justin in place so events can reasonably be considered to be favourable.
So, perhaps a little earlier or later than in canon (3028-3029) Hanse uses some variant of Operation Galahad to pre-position his regiments and then slams down attacks roughly equivalent to the First and Second Waves of Operation Rat. He then proceeds more cautiously with something along the lines of the Third Wave, showing signs of being low on supplies and strained by also supporting operations on the Draconis Combine. Operation Riposte/Ambush should be a reasonably likely outcome, which severely hinders the Confederation's ability to counter-attack.
At this point Hanse has cut the Tikonov Commonality away from the Confederation, with reasonable odds of convincing Ridzik or someone else to rule it as his puppet. He has Tikonov itself as well as several less important industrial worlds. The CCAF is too badly hammered to prevent him from consolidating his position, particularly since the Free Worlds League is virtually guarenteed to be putting pressure on their borders. The DCMS has fed a fair number of its forces into the meat-grinder that is the Wolf Dragoons, probably preventing any serious offensives on their part for a few years. Oh, and Michael Hasek-Davion has pretty thoroughly driven the fence post up his own arse. As a sweetener, he might very well have Justin still in place and Theodore has probably not proven himself to Takashi and the DCMS.
Without the canonical Fourth Succession War to compare to, I can't see how this would look like anything but a glorious triumph to the Inner Sphere. The AFFS is worn down a bit, but with the CCAF and DCMS both similarly exhausted Hanse has time to restore it to strength and do any fine tuning he might want to do based on after action reports. At that point he's free to either make a further attack on the Capellans or turn his attention to whatever worlds the DCMS may have taken during this conflict.
