The Shulhan Aruch (Siman 309) discusses a case of a child holding money in his hand. To what degree do the Halachot of Mukse limit handling the child? Maran records a Yesh Omrim (minority opinion) that the child's parent is even prohibited from holding the child's hand and walking with him, out of concern that if he drops the money, the parent may instinctively pick it up. However, the Stam (unattributed) opinion cited by Maran prohibits only to carry the child. Even, if the child needs to be held by the parent, he must first drop the money.
In a case where the child is carrying a different Mukse item, such as a stone, the same Halacha applies. It is prohibited to carry the child as long as he is carrying the Mukse. Holding a child who is holding Mukse is tantamount to holding the Mukse oneself. However, Maran is more lenient in this case and allows the child to be picked up, if he has severe pangs of needing comfort and refuses to release the stone. There is less concern that the father would pick up a stone, as opposed to picking up the money.
SUMMARY
Holding a child who is holding money, is never permitted, even if the child is very upset. If the child is holding a different Mukse object, it is still prohibited to pick him up, unless he refuses to release the Mukse and is severely upset.