Been round this buoy at great expense several times (not least to theft).
Now have 3 and 6 yrs boys.
Phase one was trailer. Worked well but tedious on the road, and even more off it, as it's a two seater and quite wide.
2. was a cross-bar seat. Full one with headrest that goes on an additional bar between headset and seatpost. Fine so long as you have a very upright position, or their head is in your chin/chest whole time. Better for them though, as they see more and you can talk to them.
3. Was seat on back. Fine to about 4 yrs.
4. Tag-a-long. I modified the seat from 2. above to replace the saddle, and took the pedals off. Probably the best on-off road riding solution by some way.
5. Tag-a-long with normal seat, as per how it comes.
6. Trail Gator. Total rubbish. Badly made pain in the ass that bent and ceased to function quickly. In essence, the method of fitting the bar to their bike at the headset it pants, and relies on little bits of bent metal. No where near strong enough, and two of them just tore. Shame as sound enough idea, but badly designed and constructed.
7. Tag-a-Long, with baby seat on the back. Works fine, but you have to be confident and have decent handling skills. Less stable than on it's own, but you can take 2 for a lot less than a double tag-a-long.
8. Tandem with foot rests on rear seat for short legs, and seat/tag-a-long on back. Works fine, but cumbersome due to length, and bloody heavy to peddle up hills.
Oldest could ride from 3 anyway, and patience for not being on own like bike limited.
In summary. Small - best is on-bike seat. Larger - tag-a-long. 1+ double tag-a-long would be best, but costly.