I suggest that you load gear into the camper that you plan to leave in it for your camping trips. Then, take it and get it weighed. Look for a nearby CAT scale facility. I think if you go to their web site, there is information on how to weigh an RV. By getting it weighed, you can see what your actual weight is and then you can determine how you need to proceed. But, using a second vehicle for the family and extra gear sounds like a very good idea. It's so much better to play it safe.
Check the tires....if they are over 5 years old, replace them. Camper tires rot out before they wear out the tread (for most folks) and you don't want to experience a blow out while towing it!
Make sure added weight to the popup is evenly distribute or have slightly more weight forward of the axle. Too much weight in the rear can cause trailer sway.
Good luck and I hope you can enjoy many great camping trips!