We loved Trysil - stayed in the Radisson Blu, which was fun for kids who had never stayed in a hotel before, always self catering. Friends stayed up the mountain closer to the slopes (you have to get a bus from the hotel) and on balance I think we would have preferred that, but the Radisson was fun as a one off. It is COLD. Something to think about with the real tinies I think. Our balaclavas all iced up every day and that is at Easter! That is where staying in the hotel and having a pool comes into its own if the smaller ones get too cold and want to come home mid afternoon. But loved the heated mountain huts where you could have your lunchtime picnic (or even cook!). There isn't much sitting around in deckchairs soaking up the sun - or there wasn't when we went in late March. We also loved the hutte where you could go for waffles and hot chocolate mid morning or afternoon, it was like skiing through Narnia to a little clearing. One of the lifts, a t bar, was pretty scary with a five year old, as if you fall off it the only way down is a black run if I remember correctly - it was quite painful having the t in the back of your knees while trying to hold a toddler upright with their skis waving all over the place! Snow was amazing, some of the best I have ever skied on. Husband needed more runs, but the rest of us (intermediate) were fine. There are some slightly nerve wracking icy narrow passages through trees, but also lots of lovely open pistes at the top. Most of the instructors were Swedish and absolutely brilliant with kids, so much nicer than most of the French or Swiss instructors (trying not to generalise) but make sure you have a group with other English speaking kids.
The booze is expensive, so we took out a wine bag on the advice of our friends who were self catering ... and then never used it. It isn't the Folie Douce type holiday and it was easy to justify buying one beer at the bar and then perhaps a glass of wine with hotel supper, but we didn't drink nearly as much as we usually do, which was surprisingly doable! Just a different sort of ski holiday...
Overall it was a great holiday - we haven't repeated it, but I wouldn't rule it out, especially for late season snow.
I hope you get your Italy trip too BeanMachine.