Hey there! reddness on the belly could be irratation from the grass... happens to my girl all the time, but if you can get a picture up it would be good to confirm that is all the issue is.
Benedryl 1mg per pound of pup up to 3x a day will help with the itching.
Gate --- we use babygates all the time, have three in the house for when they need to be blocked off but not out of site.
What you can do, is keep him behind the gate until he gets all the new scents and then leash him and allow him to smell everyone while you can control him. Once he has a scent and all is settled, you can remove his leash, if it is too much for him then leave behind the gate or leashed whichever you are more comfortable with. Also, weather permitting let the visitors take him for short walks .
GOOD LUCK and keep us posted