If someone in your family has down syndrome, is there a larger risk that your baby will have down syndrome?

Slight risk. Most down syndrome is sporadic. A few patients with down syndrome have the extra 21 chromosome translocated on to another chromosome. In some of these cases the parents can carry the translocated chromosome in a balanced form and they and other family members could be at increased risk to have children with the syndrome.
Yes. A clinical geneticist will inform you that your empiric risk is approximately 1 in 100 because of the history, so prenatal diagnosis is indicated. A revolution has occurred over the past year. Maternal blood for free fetal DNA analysis, with 99.99 % accuracy, from 9w0d or10w0d, results in 7-10 days for trisomies 21, 13, and 18. For people without insurance, one company charges $25--150.
Downs syndrome risk. In general, downs syndrome does not run in families. Risks appear to relate to maternal age at the time of pregnancy.