I'm guessing you're from a different country and I'm perceiving that we might have some cultural differences. However, regardless of that, I'd advise letting some time go by while the dust settles with their relationship. Particularly because she cares about her ex and vice versa. The fact that she's in this tender emotional state AND her parents were the catalysts for the breakup .... this means you should keep out of it totally and just be friendly.
Your comment about you 'looking at her for 4.5 yrs.' and you think that she's been checking you is not relevant. It is unclear what these looks mean. What does matter more is being respectful of her feelings and her need to recover from the breakup.
You can't lose someone you never had...as her heart is already involved with someone else - no matter whether or not their relationship has been affected by parental intervention.