Was david's son's cursed for his sin with bathsheba?

Because of David's sin with Bathsheba and his unjust order that led to Uriah's death, Satan was able to bring evil upon him. Nathan prophesied about the resulting outcome in II Samuel 12.

II Samuel 12:13-18 "And David said unto Nathan, I have sinned against the LORD. And Nathan said unto David, The LORD also hath put away thy sin; thou shalt not die. Howbeit, because by this deed thou hast given great occasion to the enemies of the LORD to blaspheme, the child also that is born unto thee shall surely die... David therefore besought God for the child; and David fasted, and went in, and lay all night upon the earth... And it came to pass on the seventh day, that the child died..."

David's fellowship and favor with God was restored, but his son, who would have been Solomon's older brother, still became very sick and died. David's return to God was heartfelt, so much so that God called him "a man after mine own heart" in the book of Acts.

Acts 13:22 "And... he raised up unto them David to be their king; to whom also he gave testimony, and said, I have found David the son of Jesse, a man after mine own heart, which shall fulfil all my will."

Following David's example, we can become people after God's own heart, regardless of our past transgressions. To the extent that we rightly divide God's Word, we live fearlessly and rise above all iniquity and sin.

II Timothy 2:15 "Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the Word of truth."