If I and my spouse divorce, she is 58, can she get SSI benefits based on a previous marriage to ours.

Generally, benefits cannot continue to be paid if the divorced spouse remarries someone other than the former spouse, unless the latter marriage ends (whether by death, divorce, or annulment), or the marriage is to a person entitled to certain types of Social Security auxiliary or survivor's benefits.
A person can receive benefits as a surviving divorced spouse on the Social Security record of a former spouse who died fully insured, if he or she:

is at least age 60, or age 50 and disabled;
was married to the former spouse for at least 10 years; and
is not entitled to a higher Social Security benefit on his or her own record.
If the surviving divorced spouse age 60 or over applying for benefits remarried after age 60, or after age 50 and at the time of remarriage was entitled to disability benefits, the marriage is disregarded. If a person is already entitled to benefits as an aged or disabled surviving divorced spouse and remarries, benefits continue regardless of the person's age at the time of remarriage.

The benefits paid to a divorced spouse or a surviving divorced spouse will not affect the benefit amount paid to other family members who receive benefits on the same record.