Complex sentence: It remains unclear of Ingrid Ylva was still alive at this point; though it is believed that she was, however, she does not seem to have played any part of the royal court, and probably preffered to stay in her estates.
Split into simpler sentences: It remains unclear if Ingrid Ylva was still alive at this point, though it is believed that she was. However, she does not seem to have played any part at the royal court, and probably preferred to stay within her estates.