Does the second wife get the same rights as the first wife?

Yes — under the Shariah, the second wife has the same rights as the first; there is no 'second-class' wife. She is entitled to mahr, maintenance, housing, a fair turn and kind treatment. 'First' or 'second' refers only to the order of the marriages, not to rank. Nor is the second wife obliged to obey the first wife; obedience in what is right is owed only to the husband. Likewise her children have the same rights of lineage, maintenance and inheritance as the children of the other wives. Make sure the marriage is registered so that these rights are protected by law. See each wife's rights.