In this situation, you may create a white lie to account for your absence. For example, that you went to look in on a sick friend or to do a mitzvah for someone who wishes to keep the details private. Your husband can help you with this. If telling a key female family member or friend will help you manage your immersion with minimal disruption or embarrassment, you should not hesitate to tell her you will be immersing.
You could also call the mikveh or mikveh attendant in advance and ask if it might be possible to arrange (probably for an additional fee) to immerse after the meal.
If you cannot find a comfortable resolution (and your husband agrees), you may postpone immersion to the next night.
Chag sameach!