It’s hard to know whether your sister is a spoiled brat who doesn’t want to grow up or mentally ill and only able to function like a child. Either way, you have more going on than you can reasonably be expected to handle. You didn’t mention if this is new behavior or if she has always been like this. Nor did you mention why she is with you instead of with your parents. I’m therefore very limited in my ability to understand the situation.
I do think you should insist that your sister have a mental health evaluation. You are fortunate to live in an area where there are many resources. Simply search on the internet for “mental health resources and your city.” There may also be an evaluation team on base for families of deployed personnel. Your chaplain may also be able to help you match your sister to resources she needs.
If a mental health professional determines that your sister has a mental illness, she’ll also be given a treatment plan. Since she is living with you and you are acting as a caretaker, do get your sister’s permission to sit in on the planning session. If she says she won’t let you, you may have to be more firm than you are used to being. You could tell her that living with you depends on her being open with you about what is wrong and doing what she can to get better. You don’t need or want to be in on every aspect of her treatment but you will probably have more compassion for her if you can have an overview of her problem and the suggested treatment.
If the professionals determine that she doesn’t have a disorder but is using you to avoid the responsibilities of adulthood, it’s time for the gravy train to end. Give her a few weeks to find somewhere to go and to go there. You have a small child to take care of. You don’t need a big one. Your husband does not need added stress when he gets home. You and your husband need to be able to focus on your own little family.
I wish you all well.