It can be very risky inserting a finger into the vent because you can introduce bacteria or even fecal matter and cause an infection.
It might be a good idea to give her a calcium citrate +D3 tablet every day for about 5 days to see if that helps, it often can. This is available at any store that sells vitamins/ supplements, it can be marketed as Citracal or its generic equivalent. Sometimes even though they seem to be getting plenty of calcium, they need the D3 to absorb it properly. This is standard treatment for hens that are dropping soft-shell or shell-less eggs. Just pop one of the tablets right in her beak, it may look big but she is well able to swallow it easily.