Hi Mary, I can't talk about a wagon since I have no experience with that. I did however purchase a jogging stroller for Olivia and it's one of the best purchases I've ever made. My dog hates to walk and is extremely fearful to boot. Add to it that I am physically challenged with balance issues and extensive nerve damage with an almost useless arm so, holding on to my furbaby on walks was painful an exhausting for me. I bought this on sale at the time.http://www.amazon.com/dp/B007WMZ7XE
Mine fits Olivia fine but if you wanted to put all three in I think you would need one like the Pet Gear AT3
I found this article very helpful in choosing, issues that I hadn't thought about but turned out to be important like size and type of the wheels and handle height not to mention an underneath area for sweater water bowl, and anything else to carry...http://joggingstrollerplaza.com/pet-jogging-strollers-and-my-top-3-list/
I also found a hands-free jogging bungee leash that makes life so much easier....especially using it in conjunction with the stroller. I bought one without the bungee as well..... All depends whether you mind them being out in front of you because the bungee gives them a little more freedom..... or on the side of you. Wish I would have known about these years ago.... http://www.amazon.com/dp/B017IIUK6U
So we start out with that leash and usually I'll put her in the stroller on the way back.... Both these things have made the walks really enjoyable. Another plus is she is much less fearful in the stroller.
Hope this helps....