@Sheryl194 Yes, you do have a very inviting backyard and I can see where the guest's wheels start spinning for hosting getogethers.
I do not suggest charging for x amount of people on reservation as this will be gamed all the time and you will be pulling your hair out.
What I would do is obviously set the expectation in your house rules and things to know that only guests on the reservation are allowed on the property and maybe an exception with permission.
I would also use a rental agreement where this is also specified and what the consequence of having more guests on reservation using the property would be. I would not have being charged for more as an option because many will just pay the extra.
I would have the consequenc be that you will be asked to leave if it is found that more guests than reservation are using the property. Something about signing their name and acknowledging the rule seems to send the message. They have been told and also told the consequence of having to leave which is more dire than paying a few extra bucks to get their way.
Also maybe you are hosting more local guests or guests that have friends and family in the area. This will often be mentioned during the booking and that would be the time to remind them of the no extra guests rule incase that is what they are planning.
Hope this helps!
Karen