How might the world be different if Anthony/Cleo won battle of Actium?
Not at all.
Antony was the senior partner in the Antony and Cleopatra alliance;Egypt was a rich country but had an inconsequential military,and Cleopatra needed Antony's powerful Roman army to keep her on the Egyptian throne,as she had needed the support of another powerful Roman general 15 years before for the same reasons.
Even had Antony won the battle of Actium,he still needed to win the war as a whole,and this meant physically controlling Rome - doubtful given the Roman attitude towards Cleopatra unless Octavian was killed or captured.If this had happened,Antony would have become the first Roman emperor rather than Octavian,but would have had to rule from Rome,or face constant challenges to his authority.Antony was a Roman and spoke Latin,and therefore his children - if they had succeeded him - would have done so to.Cleopatra would eventually have died,so any control or political influence she had over Antony and her children would have died with her.The Roman empire would have been run from Rome with a Roman cultural slant;Rome was the dominant regional power well before Actium,and would have remained so afterwards,militarily and cultural,whoever won the battle and war.
In terms of religion,Romans were tolerant of other faiths as long as they presented no overt political threat,and the cult of Isis - an Egyptian goddess - remained popular throughout much of the empire well into the Byzantine period.
The werewolf does not have to be risque. Just get a tiger striped top, a cute jacket, some cute leggings (maybe animal print), and a skirt. Add boots or flats and there you go! For the hair, just use a curling iron.
If you must do Cleo, then you can just get khaki capris and wrap surgical gauze (you can get in first aid at Walmart) around your daughters wrists, ankles, and around her waist like a belt. Get a lot of gold bracelets. Get a halter top to wear in a brown color. For her hair, use spray on blonde and brown and make stripes in her hair.