Firstly, we empathise with your experience. The ferries making this trip are point-to-point carriers and thus are not obliged to refund when leaving or arriving late. Tigerline offer the last ferry trip from Phi Phi to Phuket each day and so is popular, but they can be subject to more delays that the ferries that depart at 2:30pm or earlier.
I understand that it's not easy having to endure transportation delays with two children. We contacted Tigerline on your behalf to see if they could do anything but alas they have not refunded their ticket price to us for the reasons stated above.
However, I am willing to extend to you a $30 USD refund in appreciation that the trip was more difficult that you had envisaged. As your connecting agent, I appreciate your feedback and will see what I can do to either close this service gap with Tigerline or provide more information to future travellers based on the information you've graciously provided.
We will issue the refund today and it should take approximately 15-20 days to reach your account so please do check your next statement.