I married a girl that came from this type of family BUT I made sure that she would commit to me over her family before we got engaged.
If you're interested in the relationship lasting, you need to quit enabling the behavior and calmly explain the choice before her. The next time she is faced with choosing to spend time with you or with siblings, you politely let her know that you're not interested in coming second anymore. Explain that she needs to decide whether she's ready to tell her family no in order to be with you. But emphasize that it's totally her choice, and you'll respect it. No emotionally charged words or pressure. Just a simple choice that she needs to make. If she'll tell them no in order to spend time with you, great. The relationship advances and grows. If she wants to stick with family first, tell her you respect that but you'll be looking for someone else to date.
Luckily, my wife understood this and quickly figured out how to tell her family to pound sand. I proposed shortly after, and we've had a great marriage.