Unique Baptismal Situations

Greetings, all...

I have a question about the variations we might see in our baptismal practices based on the unique situations we come across as pastors.  

Normally, as our Reformed understanding of the sacrament has guided us and our church order teaches, baptism is a sign and seal of the covenant promises of God given to children of believing parents, and to non-baptized adults who make a professon of their faith. Baptism is a picture of his grace shown through Jesus Christ, as well as a challenge to the parents to do all they can to lead them through word and example to be followers of Jesus Christ. Parents embrace this challenge by saying:  "We do, God helping us." We also know that the sacrament is carried out in the context of the Christian community - usually, during a worship service.

I'd be curious to know, however, how have you addressed the unique situations?  What about when a grandmother requests baptism instead of the mother?  Or if a baby is not long for this world?  What about when baptism is requested to be administered not during a worship service but more privately, such as at a hospital or a nursing home?  What about when someone who grew up in another church tradition requests being re-baptized because they didn't see their previous baptism as legitimate?

I know where I stand on some of these examples which I've taken from different moments in my ministry or from situations shared by others.  Someone's desire for baptism can be a call to faith, an opportunity for discipleship or education about what the church truly confesses.  But on others, I find myself a little less sure because it seems that baptism could be a powerful witness to God's gracious love during moments when life is messier than usual or when a person's history doesn't fit everyone else's story.  

I remember during my Classical exam one of my questioners tried to place me hypothetically in an "Ethiopian Eunuch" situation where I picked up a hitchhiker who accepted Jesus while we were driving, and while we were passing a river, said:  well, it happened in the Bible, what's to keep me from being baptized right now?"  The big question before Classis was:  "How would you handle that, pastor?"   I responded by saying:  that would be such a cool moment, to stop and spontaneously jump in the river and baptize that new believer.  But noticing the grimace of the questioner, I added:  But I know I'm also responsible to my council and know that baptism is a sacrament given to the church, and is celebrated and goverened by the church as a whole.  Or something like that.  Then the questioner smiled.  :-)  I was "in".  But the tension of that question has never left me.

I will admit that my question has been brought on by a recent request, the details of which I won't divulge in this public forum.  But I am curious if you have any stories from your experiences you might be willing to share that might address some of the unique baptism requests or situations you have encountered, how you handled them as a pastor or council and how they were "resolved" or carried out.  

Thanks in advance for any stories you might share.