Which is why I posted that it is very important that the funeral director/home be aware of incoming family members, flight numbers etc. It is also important that arriving family members have telephone contact information with the funeral directors so that schedule changes can be made.
Changes in schedule are not unusual. It is a rare situation where a church, funeral home or grave side service at a cemetery cannot be delayed for a period of time without causing problems. It sounds as if in this situation that a delay of 90 minutes would have solved the OP's problem.
This is part of what you are paying for folks!
The methods of delays can be subtle from slowing down the rate at which people are able to park their cars to assisting people to their seats at a slower pace. Most people attending a funeral are not aware of such changes in schedule.
The OP's arriving family members should have been given a telephone number to call if they had problems in flights and even to say 'we are here'.
Also the OP should have told the funeral director that important members of her family were delayed and asked for assistance. All those nice looking professional funeral folks are there to lend assistance and not just look nice.