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I went through similar things with my x wife when I used to have vistiation with my children. While I can not tell you what to do, I can tell you do not record the phone calls as it is illegal to record any phone conversation that is not with you.

In my opinion you may limit the calls without making yourselves look bad. Maybe allow the calls to come everynight, at bedtime, just to check in an say

We have limited the calls to once a day after we pick her up from daycare and before arriving home. Do you think that limiting the calls further to every other day would be ok? She has the contact information for the daycare and does call them daily to check on how my stepdaughter’s day is going.

Limiting phone calls to every other day may be construed as reasonable, but I cannot predict what any one judge would consider as reasonable in any given case.