“Reasonable” is open to definition, and this is usually determined by whatever the judge is persuaded to deem reasonable. You make a fairly good argument for “unreasonable” as to the supplemental baby-sitting. However, you really should speak with an attorney about how to approach this issue. I know you want to support your child but that support should be reasonable and not excessive and indulgent of mom, even if you have a good salary.
Best of luck to you.
This response is intended to be a general statement of law, should not be relied upon as legal advice and does not create an attorney/client relationship.