Quiltingfan, I sew/quilt a lot in a travel trailer (although not with 3 teens and animals!). However, I'm sure you can do it! I found it important to be very organized, and make up kits ahead of time. I keep everything for the kit (cut fabric, pattern, thread, etc) in large zip lock bags, and I keep all of the kits in a box. I also use a small 2-sided pressing/cutting surface (12" square) and a small travel iron. I have a rolling bag that has my smaller travel sewing machine and all of the basics, plus the iron and pressing mat. See, only two things to store and haul out!
I sew at the dining table when my husband is out doing his "thing". I'm sure your teens and hubby will find something to keep them busy during the summer, oh, and suggest they take the animals with them :-)