Hello Frank,
I went to www.rootsireland.ie and found a baptismal record for Robert Cross, father Samuel Cross, bap. 1900 in Co. Wicklow. I then went to the co wicklow site and searched for the parish. I found the record in Ballinaclash COI (Church of Ireland) . It seems the family were protestants. This makes the searches a little easier as the names are a bit more unusual.
I searched for a marriage record for Samuel Cross and found one in 1899 in parish of Dunlavin COI .
You will need to pay to view these , about €10 for both but it will give you more information regarding Robert's mother.
As there are so few families with the name Cross you would be wise to read each one carefully and not dismiss them for whatever reason.
If Anne was the name of Robert's mother, hopefully you will find tht on the baptismal record. According to the census she was probably born around 1873 +- 2 years or so. If they were married in the parish of Dunlavin then she must have been from that side of the county. (It was customary and still is in many places to marry in the bride's parish).
I hope this helps you in some way Frank. It's all detective work, but it's strangely addictive!!
Anne Dennehy