You may be right that your DIL is being messed around because of the other scenario but I'm not sure how linking them in any follow-up discussion regarding the late payment is going to help - it just muddies the water.
The employer is in breach of the contract for not paying an employee on time, the typical claim for which is payment for any knock-on loss incurred because of the breach.
So if she's incurred bank charges because money arrived late, that could be worth pursuing. IMHO it's probably pushing it to claim for loss of time and travel costs - she offered to go in to collect.
Perhaps write to employer to state how inconvenient the occurrence was, and close with 'I trust that this lapse was a one-off.
What else were you expecting?