I don't think this part of the family ever got involved with Carlism... to start with, this Bourbons are not dynastic, as Enrique María's marriage to Elena de Castellví y Shelly was morganatic, thus preventing their issue to reign.
Enrique María was King Francisco de Asís's younger brother, so even when Enrique's relationship with the Royal Family was not a good one, himself being a liberal and "republican", I don't think he or his children would have never had sympathies with carlists!