We did reno few years ago, replaced with Costco Water Ridge Dual Flush Toilet, LD does not like it that much (he thinks it does not flush solid completely ), but I am fine with them, it is one piece, easier to clean.
Now for the seat and cover, the thing is that you have to put the cover down (not just the seat ring) in order to flush, (the fluch is on the top, not on the side) So my kids never had this issue, in fact, they keep the Toilet coverd all the time :-)
Another thing I like them, it is slow release cover so it is very quite..
Anyway, I feel your husband is bit over reacting, he might had bad sleep that day? I think your boys are great that they lift the seat up first, instead of just doing it with it, don't you think?