As a second wife, am I entitled to separate accommodation from the first wife?

In general, each wife is entitled to reasonable, separate accommodation in keeping with the husband's means. Islam requires a husband to provide a home that protects each wife's dignity and comfort, not to force two wives to share one roof without their consent. If you are worried, check the conditions agreed at the marriage contract (akad nikah), because the Prophet ﷺ said: “The condition that is most rightful for you to fulfil is the condition by which you make lawful the private parts” (Sahih al-Bukhari 2721). Discuss this need with your husband kindly first. If this right is neglected and discussion reaches a dead end, the Syariah Court is the right place to assess your claim. See relationships between co-wives.