Personally I’d look at a cheap generic 3 or 4 person Kelty. Not very light but with kids that young you won’t be hiking dawn to dusk like thru hikers. A couple years ago I took a 9 year old caribou hunting. He got tired so I took his rifle and I think his water in addition to my rifle, the spotting scope etc. I probably had 30 pounds. I still had energy to hike when the reasonably fit kid started to tucker out. I doubt a heavy tent will slow you down.
Side note, hiking gets old faster for littles. Plan fun campground activities. First pocket knife, s’mores, etc. When I was 4 or 5 I put a Donald Duck butter knife in a leather sheath I found somewhere and that was my “real” big kid knife. I could peel bark off a stick and that was pretty cool for a preschooler (but not very dangerous). You might be able to do something similar. I like to have a few surprises I pull out at opportune times.