This question comes up often when I'm consulting with pet parents prior to an in-home euthanasia. I think it is important to recognize that there probably isn't a correct answer to this question and that every situation and circumstance is different. Some animals may not be very concerned with the passing of another pet in the house, while others will show signs of concern and later even exhibit signs of grief or depression after. Each pet is unique. In practice, however, I think it is important to allow other pets in the household the opportunity to use their specialized senses to understand what has transpired. This can be done by allowing the pet to remain present during the passing as long as the pet is not going to cause disruption or disturbance to the process. I do believe that the pet should not be forced and should always have a way to escape if they need to retreat. I think this is a good idea for their human counterparts (including children), as well. No one should ever be forced to be present during a loss as significant as this if they feel they are not able to. It does not mean that you are not strong or that you do love your pet.
If the pet(s) are disruptive or causing stress on the family, then removing them until the euthanasia is complete is a good idea. At that time, when the pet parent is ready, the pet(s) can be allowed back in so they can assess what has happened. Just remember, every pet, like humans, will react differently. Some pets may not show any interest at all. This is ok. Just remember not to force your pet to grieve the way you feel they should. Animals are amazing creatures with the ability to sense loss too, it just may be in ways we don't always see or understand.