Let’s see if I understand you correctly. You joined your current parish out of the belief it would save you money on your child’s school tuition to do so. Now that you’ve discovered that you can receive the same tuition discount if you are a member of any parish in your diocese, you have decided you don’t like your current parish and feel no sense of responsibility to it, even though your child attends its school. You therefore want to join another parish you prefer.
Parishes should not be treated like your local Starbucks, where you can browse the selections, take advantage of deals, and go to another location whenever it’s more convenient or preferable. A parish church is to the universal Church what a nuclear family is to its extended family, the place within which a Catholic makes his home. There can be times at which a move to a new parish is necessary, but such a move should not be undertaken lightly and without due consideration for the needs of and responsibilities to the previous parish.
In your case, I assume your child is still attending the school run by your current parish. If so, and if that school continues to meet your child’s needs, then you should feel some sense of responsibility to the parish that runs it. That doesn’t mean that you cannot attend another parish on occasion, or even that you are forbidden from registering at another parish if you’re determined to do so. It only means that your attitude toward your current parish is problematic, considering that you intend to keep your child in its school and accept the tuition discount you’ve been given.