I remember those days!
Kids + TLS does not compute! Teddies, Capol, pens & paper, large sleeping bag, etc, etc, etc
Daughter was 7 here I think. Perfectly capable of riding but not able to cover the distance hence the tow bar. We'd been 'touring' with it from age 5 but this was the last trip as I was starting to loose my patience. Didn't help that she is quite tall for her age.
I started with a trail gater but had the same experience as you and very quickly gave up on it. Looked at a follow-me but too expensive so in the end we used a trail angel with some success. Not perfect and they are quite heavy but work much better, managed 4 days and 84 miles fully loaded (daughter riding and being towed) without much issue.
It does get easier...
A year later and 86 miles over 4 days but still sh*te loads of stuff!
The biggest issue I have now is the frustration of mismatched ability, especially if you need to crack on (e.g. had a mechanical and need to get somewhere). Not much you can do about that, just have to remember to chill and enjoy the experiences together (often easier said than done!)