I have worked for social services, admittedly in an administrative capacity, but it did mean I got to see planty of case files.
Believe me, the social worker's concern will be for the welfare of your daughter, although if her behaviour appears to put herself or your other children at risk of harm, then the he/she is duty bound to intervene - it's not just a matter of being interfering. In any case, social services usually like to know about siblings etc because then it gives them a better idea of the family dynamic. Social workers are not out to seperate you from your children. They are highly trained and experienced and genuinely care for those individuals who make up their caseloads. They can also be the key to getting further help, both practical and financial.
The problem with social work is that it only seems to become high profile when it goes wrong - the Victoria Clambies of this world, for instance. But there is so much social work going right and making big differences to people's lives.
If you're concerned about that first interview (which will most likely just be an 'assessment' interview), then call the person who's going to be interviewing you and ask them what to expect and whether you should take your daughter. You may have to leave a message (perhaps with someone like me), but the team I worked for were pretty good at returning them.