I've been using a bike + trailer for the past 3 years for hauling kids + stuff and general car - liteness.
I've never used an xtracycle, but I can offer a few observations about kids and trailers:
Weather protection is pretty easy with a trailer. Rain, shine, or snow, the kids don't care. Blankets for when it's cold.
If the bike goes over, the trailer stays upright.
Low-speed handling of the bike is completely unaffected by the weight in the trailer. No wobbles when climbing.
Napping en-route is easy in a trailer.
Braking is a little trickier with trailer, as it tends to 'push' the rear end of the bike. So, more use of the rear brake is needed.
A trailer means double the rubber on the road, so there is a noticeable increase in rolling resistance, compared to carrying the same amount of weight on a 2 wheeler.
Trailers are wide, so can be pain to fit around gates on MUPs and through doorways.
It is possible to flip a trailer by clipping a curb, bump or the like while cornering at speed. I've done this once when I was hauling stuff (not kids) and I was in a hurry. If you watch your speed, this isn't an issue.
If you are using it to take the kids to school / nursery / wherever and then going on about your day you can just lock the trailer up and leave it with the kids. This way, you are not pulling around cargo capacity that you don't need.
Communication with the kids while they are in the trailer is difficult. Especially when the rain-cover is fitted and there are cars about.
A good quality trailer will address all the issues you mentioned regarding straps, push - pull feeling, etc. They also tend to be less tippy in the corners.
When it's windy, a trailer is a sail (this is good or bad, depending on the direction of travel
)
I'm paranoid about drivers seeing the bike, but not noticing the trailer. I haven't had any close calls, so maybe this is just in my head.
Hope that helps!
FWIW, I've been revisiting my situation with the trailer now that the older kid is 4. The trailer is getting a little crowded... I'm considering a longtail, but the lack of weather protection is putting me off. All in all, I've been totally happy with using trailer up to now though. The kids like it, it's fairly versatile, and I can use it on any of my bikes if the 'tractor' is out of service. Speaking of which, I got tired of constantly hooking up and removing the trailer depending on what kind of trip I was making, so I got a used bike cheap that I just leave the trailer attached to, and then use my other bike(s) for non-trailer trips.