Both parents contribute equally--it is not a case of the male being dominant or the female being dominant. It depends on the particular allele each parent contributes for each gene.
Assuming that the ameraucana is a true ameraucana, she should have two copies of the blue egg gene, so all her offspring should lay a blue eggshell. Since papa is a brown-egg laying breed, he will contribute the genes for brown to the eggs, and they will be some hue of green: a blue eggshell covered by brown pigment. If mama is not pure for lue eggshell, only half her offspring will inherit the trait. Since there are so many different genes (at least 13) that go into creating brown eggs, chances are that even if several are missing, there will be other present that will create brown eggs. The vast majority of egg genes are not sex-linked.
As for the feather colour, you'll have to provide more information on the parents for us to be able to predict the offspring. Photos would be good.