Your best recourse is likely with your landlord and not the police.
While many municipalities do have noise ordinances that are enforceable by the police, the focus of these rules is typically commercial noise--early morning or late night construction or music from night clubs--that may causes an unreasonable disturbance to neighboring properties. As the police you spoke with noted, a rambunctious 3 year-old will not likely be covered by the town's noise ordinances.
You do, however, have rights to the quiet enjoyment of your home. In apartment complexes, there are typically rules and regulations contained in the lease or in an attachment to the lease that all tenants are given when they signed the lease. Excessive noise is often covered in these rules.
Your landlord or the property management firm handling your complex is tasked with administering these rules. You should talk to them about your noisy neighbors. If they can't resolve the issue amicably with the neighbors, perhaps they would be willing to move you to another unit in the complex (perhaps one on the top floor).
There is little legal help that can be offered to you based upon your description of the situation. You can speak with your building management about the difficulty but it is unlikley that you could defend breaking your lease given that the noise is during the day and is not due to unreasonable activity by the upstairs tenants. Perhaps a different approach would be more productive, rather than confrontation, take over a cake to welcome the new-comers to the building or loan the youngster use of books or movies that your children enjoyed (quietly). Good luck.
The information provided to you in this answer is not, nor is it intended to be, legal advice. You should consult an attorney for advice regarding your individual situation if you have further questions.