Strange Request?

[Lee-Bee]

Totally normal. it is up to you to decide whether or not this is something you want to accommodate.

I don't as it is just too much to handle, the kids all act differently, depending on the kids you have I've had kids that out right scream in terror at the sight of other adults and there is just no way any one benefits from that.

If they can't take the leap of faith that I will care for their child without them visiting during daycare hours then they are just not a good match for me.

Just explain your reasoning and leave it to them to decide if they wish to proceed. I just explain it from the children's perspective (some are scared of new people and this is their safe zone), let them know that by letting them do this it means you would be doing the same with future potential clients meaning random adults in contact with their child.