I'd be careful of the unprotected sex part. I have a friend that decided to divorce her husband after their first child, but stayed with him long enough to have a second child. She had no intention of working out their problems. She wanted their first child to have a sibling with the same father. She divorced him soon after their second was born.
The sex part is good though, although I don't think having another child will do much to help your situation. Just be cautious of the whole biological clock idea mentioned previously.
