Single mother joining army?


So I’ve enlisted in the army and was wondering of woman with the same story and need feedback. I have a 2 almost 3 year old and while I can still join with him. I have to give my rights up for basic then get him back after ait. Now my recruiters told me that they thought since I was a single mother, I’d have to live in the barracks and him at home with my family until I got married to recieve BAH. Is this true? Is there any single mothers in the military that receives BAH to live with just you and your child?