I don't think that is a reason for it to fail. A thing can be an Arcane Connection to many other things. Just like a photograph can capture the image of several people.
Practically all Arcane Connections are Arcane Connections to several things.
For example, a brick is an Arcane Connection to the wall that it came from, the quarry that the stone came from, the mason that laid it, and the city that the wall surrounds. The rate at which each of these Arcane Connections expires could be different. So, by the time that the brick has been laid, it may no longer be an extant Arcane Connection to the quarry, for example. If you want to use the brick as an Arcane Connection to aid penetration against the mason, then use it with an appropriate spell. If you are speculatively casting to find out what is at the other end of an Arcane Connection, then what you get will depend on the spell that you are using. An Intellego Corpus spell to query "who the mason was" is not going to return an answer of "the city wall". If two masons worked together to lay the brick, then whichever one is more "strongly" the mason will be returned. If both equal, then one or the other will be returned (perhaps unless it is a Group target effect, in which case it will return both).
The spell doesn't need to do anything. It is the spell caster who uses both the Arcane Connection and the spell. The spell caster knows which kid is which. The spell caster is trying to find the kid "John" that is missing, not one of those kids ("Stanley", "Sally", and "Simon") who are standing over there. The caster has an Arcane Connection to "John". The fact, that he also has an Arcane Connection to the other children is irrelevant.
It is exactly like having a photograph of a family trip to the beach. If one child goes missing, you can use the photograph to identify that child to the police. The fact that there are other children, a seagull, and a beach ball, in the photograph does not mean that the police are triumphantly going to say "Madame, I believe I have found your child, she is standing beside you!"
Having said all that, I don't think that a mother is an Arcane Connection to her child. The rules pretty clearly state that being a blood relative is a Sympathetic Connection, not an Arcane Connection. Being Mother and Child might be an argument for a +2 instead of +1 Sympathetic Connection, though. The placenta and umbilical cord are likely Arcane Connections to both mother and child. But only until they expire.