I have booked my first flight on EI from ORD to a UK regional airport with the TATL segment in business (P). The email confirmation is quite clear that the ORD-DUB checked baggage allowance applies throughout and also that the Stobart carry-on limit applies throughout. Presumably if one was allowed to take a second and/or larger carry-on on the ORD-DUB segment then it would have to be checked in DUB either at the counter or, possibly, at the gate. On the return any excess carry-on would presumably be checked through to ORD at the point of origin.
The web site was less clear about the change/cancellation fees but an agent assured me that the TATL rule applies. That is no fee for changes just any additional fare and a 15% fee for cancellation and refund. These are both more generous than I am used to on AA/BA!