Jessie waits for Frank at the hospital, so the two of them can see Okla. She arrived before Frank because Okla knew how to have her contacted, i.e., he already knew her prior to being 'introduced' to her by Frank in the hospital.
Recall that Jessie arrived at the hospital before Frank when they went to visit Okla (see the screen capture above); this implies that Okla knew how to have Jessie contacted. What's going on is that Okla already knew Jessie, prior to the hospital visit; in fact, Okla is involved in a scenario whereby Jessie, who cannot have a child naturally, can first obtain a male partner, Frank, and then acquire a child, all via Leo. What Leo is to get out of the deal is the 'use' of Frank, in order to make money from Frank's thefts. Jessie knows she needs a male partner, i.e., a prospective father, to look better to an adoption agency. However, since she also knows Frank is a former convict, she actually knows ahead of time that they will not qualify to adopt - that's why she suggests to Frank that they leave the agency they visit, right after Frank tells the worker there that he was in prison. She must go through the motions of going to the agency in order for things to appear normal to Frank, but in reality she knows she will ultimately have to get a baby illegally through Leo. As indicated above, from Leo's perspective, Frank is a necessary part of the whole arrangement, so that Leo will get something in return for providing Jessie with a child.
Jessie wouldn't have waited for two hours for Frank to show up at his nightclub to meet with her, if she wasn't Hell-bent on acquiring a child - note the exasperated look on her face (as shown at left) while she waits for him.
Recall that Leo at one point says to Frank that he provided him with a family - he's referring to both Jessie and the baby, not just the baby. Finally, recall that it was Jessie who suggested naming the child after Okla (whose real name was David) - this is further evidence of a pre-existing relationship between her and Okla.
