The scriptures say that the Apostle Peter was married and that she was lead to martyrdom in Rome. I would like to know as much as possible about Peter's wife. Was she traveling with him all the time? Did they have children?

We do know that Peter had a wife. During His earthly ministry, Jesus came to Peter's house and healed "his wife's mother" (Matthew 8:14And when Jesus was come into Peter's house, he saw his wife's mother laid, and sick of a fever.
See All...- 5; Mark 1:30-31 [30] But Simon's wife's mother lay sick of a fever, and anon they tell him of her. [31] And he came and took her by the hand, and lifted her up; and immediately the fever left her, and she ministered unto them.
See All...). This proves that Peter had a wife.

In 1Corinthians 9:5Have we not power to lead about a sister, a wife, as well as other apostles, and as the brethren of the Lord, and Cephas?
See All..., Paul asked, "Have we not power to lead about a sister, a wife, as well as other apostles, and as the brethren of the Lord, and Cephas?" Cephas was another name for Peter. In this verse it speaks of him leading about a wife. Most likely, this meant that he took her around with him to different places as he traveled.

However, as to the scriptural record, this is all we know for sure. The only possible reference to a child is in 1Peter 5:13The church that is at Babylon, elected together with you, saluteth you; and so doth Marcus my son.
See All... where Peter refers to "Marcus my son." This is probably a spiritual reference to John Mark. However, there is an outside chance that it could refer to a biological son.

The story of Peter's wife's martyrdom is later tradition and is not mentioned in the Bible at all. Other traditions give her different names and refer to various children, but they are all tradition and are very suspect. I prefer to stay with the Bible. At the most, we can except some very strong traditions as possible. However, the traditions concerning Peter are just too late and have too many contradictions among themselves to be of any value.