I am not an expert on such matters, but I have read many answers to this sort of question. This can be summarised as:
IF the return ticket was booked as a single trip you MAY have the whole balance cancelled.
Given the scenario you decribe there are probably too many possibilities to be sure of what the outcome will be without actually asking.
The travel website MAY be able to advise you, but such sites MAY not offer much support and, unless you can get their "opinion" in writing you'd have no defence if they turned out to be wrong (and even then that may not work).
In such a case I would personally seek written confirmation from somebody in the "link" whose answer should be binding. You could start by doing this anonymously - and may get success without having to give them details of the actual flights involved. In some cases, adding the domestic link may have made the overall journey cheaper (quite common) and removing it may increase the cost. If you started with the local airline they may be obliging - they are probably making money from the change.
Not giving your ID while you establish options is wise, if achievable, without casuing additional problems - this is neither dishonest nor against the rules - I have had experiences in life where asking people about options, or lack of them, has triggered circumstances which were counterproductive, regardless of my intentions.
FWIW - on an "around the world" flight my daughter was scheduled to fly from Dublin to Munich but decided to instead fly Dublin-Amsterdam on another airline and rejoin the flight at Munich. Unaware of the consequences she inquired of Lufthansa in Dublin, was told that they would cancel her whole ticket if she did so and then not only did so (prior to her making the other flight) but also annotated the record with statements that it must not be reinstated. She being young and very charming managed to sort things out in due course in Munich. Lufthansa has lost several customers for life and hopefully a few more every time I tell this tale (regardless of what the rule book said).
On another occasion, QANTAS gave me a "free" flight Sydney-Brisbane when I missed a flight through no fault of my own but it was NOT linked to the main ticket (NZ-China-Australia) and I was not aware of the consequences. I told them how wonderful QANTAS was and I was sure they could sort something out, and they did. Hopefully telling that gains them customers :-)