I was married to my late husband for 19 years. I remarried before I was 60 years old. If I divorce now, can I collect on my late husband's social security? And if I did divorce and collect on my late husband's social security, could I ever remarry and continue to collect ?
Yes, if you get divorced it sounds like you could potentially qualify for widow's benefits on your prior deceased husband's record provided that you meet the other requirements for entitlement: https://www.ssa.gov/OP_Home/handbook/handbook.04/handbook-0401.html. And yes, if you remarry after age 60 your marriage would not affect your ability to receive widow's benefits based on a previous spouse's record.
It sounds like you may have a number of different options available to you with regard to Social Security, especially if you could also qualify for benefits based on your own work record. You may want to strongly consider using our maximization software to explore and compare your options in order to determine your best strategy for claiming benefits.