All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
It is forbidden in Islam for a woman to travel without a mahram or husband, and it is forbidden for a marriageable (non-mahram) man to be in seclusion with a woman who is not lawful for him. {C}
Ibn 'Abbas narrated that he heard the Prophet say, “No man should be alone with a woman unless she is accompanied by a mahram, and no woman should travel except with (accompanied by) a mahram.” [Al-Bukhari and Muslim]
Accordingly, it is permissible for you to perform ‘Umrah with your previous wife while being accompanied by your sons who have reached puberty, and you mentioned that the youngest of them is sixteen years old. They are considered mahrams for their mother and it is permissible for her to travel with them. Their presence with the both of you is an impediment for the occurrence of forbidden seclusion.
Nevertheless, you should be fully reserved and avoid falling into prohibitions such as being alone with her, touching her, looking at her with desire, and so forth.
Allaah knows best.