There are a few things to consider as to why the Lannisters would not want to ally with those regions, and those regions likewise have their own reasons...
- The Starks rebelled against the crown when their liege lord was executed unjustly by Joffrey Baratheon (who was under Lannister control).
- Sansa Stark was held captive at Kings Landing and suffered both physical and mental abuse under Lannister control.
- Robb Stark and those loyal to him were betrayed and murdered at the Red Wedding, which was a Lannister plot.
The lords remaining in the North are now loyal to House Stark once again. The animosity between the Starks is too great a thing to overcome from both sides. However, Cersei did send Jon Snow a letter telling him to come bend the knee. Granted I'm sure Cersei did not expect a reply.
- The Lords of the Vale still believe that the Lannisters were responsible for the assassination of their liege lord (we as viewers know different).
- Littlefinger double-crossed Cersei by marrying Sansa to the Boltons, and then eventually helped to overthrow of the Boltons who were appointed by the Lannisters.
In the end the Vale is currently under the control of Littlefinger. Considering his motive is to "sit on the Iron Throne", agreeing to peace terms would put him farther from this goal. In Cersei's eyes the Vale has allied with the Starks, so see above.
Goodness where to start with this one...
- Lannister bannermen raped and murdered the Princess Elia Martell and her children.
- Jaime Lannister infiltrated Dorne to kidnap his niece, who was betrothed to the heir of Sunspear, thus breaking a tenuous peace alliance.
- The ruling Price of Dorne was murdered by his own people for not seeking justice against the Lannisters for the above and for the death of Oberyn.
- The new leader of Dorne (Ellaria Sand) has the Princess Mycella murdered.
- Dorne allied itself with Daenerys Targaryen and helped her start the incursion into Westeros.
- In response Cersei has the Ellaria captured, murders two of her daughters, and poisons the last one.
Let’s just say there was no way in hell any peace was to be made there!
Cersei vs. Daenerys
- Cersei believes herself to have the upper hand in the fight against Daenerys. Even Tyrion admits that for the past couple decades House Lannister has been the true power in Westeros with an army to back that claim up.
- She has fairly easily defeated two of Daenerys' strongest allies while making a new one of her own with someone who has promised and proven loyalty to House Lannister.
- Dragons have been extinct for roughly 200 years. No-one truly knows (well, now they do) what these dragons are capable of. Even so Cersei still has made preparations to deal with the dragons.
- Aegon had three dragons, yes, but he also had three capable riders. Daenerys has one at best, herself.
Cersei has nothing to lose at this point. All her children are dead. She is making a final stand. Nothing, not even dragons, are going to stop her from trying to rule.