This probably surprises you, because "Bloody" Mary is considered the first queen of England to rule in her own right. Well, you'd be right. Matilda never got a chance to be crowned. Stephen of Blois, a grandson of William the Conqueror, rushed across the English Channel and seized the throne, claiming that his ability to rule should take precedence over his earlier oath of loyalty to Matilda. (That's Stephen getting crowned on 22 December 1135.)
Matilda and several supporters were not going to stand for this, and a period of civil war called "The Anarchy" ravaged England from 1138 to 1153. (If you use the term "The Anarchy" in the search field on this blog, you'll find several consecutive posts going into detail.) But back to Adeliza.
Adeliza remarried and lived with her husband, William d'Aubigny, at her castle Arundel. William was a supporter of Stephen, and therefore would not acknowledge Matilda's claim to the throne. Adeliza, however, welcomed Matilda to Arundel, along with Matilda's half-brother (one of Henry's many bastard children), Robert, the 1st Earl of Gloucester (a king's illegitimate children were still royal, and could be granted titles and lands). Robert was opposed to Stephen as well, and some histories say he was a strong candidate for the throne but for his illegitimacy.
When Stephen learned that Matilda and Robert were at Arundel, he besieged the castle. Adeliza then took the two captive and handed them to Stephen. The assumption by the chronicler John of Worcester is that she feared losing all the properties left to her by her late husband. According to him, "She swore on oath that his enemies had not come to England on her account but that she had simply given them hospitality as persons of high dignity once close to her."
Despite handing them over to show her loyalty to the man who held the throne, she persuaded Stephen that Matilda was no longer a threat. Stephen relented and allowed them to go to Robert's castle at Bristol.
What happened to Adeliza after that? We have very little information, except that she left her second husband and entered a monastery in Flanders, whose records mention her death in 1151.
Now about this Stephen of Blois...