How do we know she got home safe from jogging?
We don't. We have two conflicting pieces of information. First, three people close to Mollie have said that her computer was in use for her online course after she went jogging, and we know that she vanished along with only those things that she has with her when she is jogging.
We also know that when she stays at her boyfriend's house she typically stops at mom's house to pick up the car before dark. We know that she had a short run around 7:30.
Putting these pieces together, it seems logical that she went for a run around 7:30 with the intention to pick up the car. We have some information about her route, but not enough information. It's quite possible that she logged into her online course before she went for a run and left the browser open during her run. That could be mistaken for being online when in fact she wasn't interacting with the online course.
My guess is that she disappeared during the run close to her mom's house, and that her online course was open on her computer throughout the evening.