The new pool in Morzine is pretty nice and was nicely full every day (ie not packed). To be honest most decent Alpine resorts have a nice Acquatic centre. The town is very quiet in summer and dominated by “stormtropper” brits, so not really a family destination I’d say.
Zermat’s fantastic but a bit wasted on a toddler as you say. Likewise Verbier, nice pool, very sunny, good restaruants.
Suggest you try something along the lake in Geneva, eg Montreux or Evian, find a hotel with a pool. Easy access to mountains (Montreux via mountain railway/car Evian via car, it’s about 40 mins to PdS resorts).
Alternatively try Lake Garda (Verona airport), Malcesine has the cable car from the town. Pretty lakeside town, swimmming in lake or hotel pool, boat trips, cable car up to restaurants/hiking … Italy is very child friendly.