Adiyen’s eldest brother-in law performs tharpanam at Mahalaya tithi for my father-in-law; but my daughter’s birth star coincides on that day. Is there anything wrong in doing it on that day?

One need not consider other aspects when one performs Mahalaya sraddham on the same tithi that one’s father has departed.
If the daughter’s birthday happens to occur on the same day, one can perform tharpanam on another day, it is accepted practise to perform it within the stipulated 15 days.
One can do tharpanam on auspicious days like madhyashtami and there is no such compulsion that it has to be done on father’s tithi; but if one is willing to do tharpanam on the same day they can overlook birthdays or else it can be done on some other day.