Couldnt Elizabeth approve her sisters marriage?

I believe because the church is against it and because she is head of the church. They could force her to abdicate.

She could have allowed it but it went against her position as head of church and so early in her reign would have set a poor tone for her rule at the very least. I think that she regretted it later on, once divorce became common within her own family. But she could not take the risk at the time.