So many people have such valuable information for you! We just did a huge family vacation (3 families) from May 7-23 this year. Four children aged 7, 4, 2 and 1. The weather this year was brutally hot, 33-34 everyday (Canadian…sorry for the Celsius)! I believe that was unusually hot. I would agree that April would be the best weather time for you to go.
I haven’t been to Uni for a while but I would question going there with kids as young as you mentioned. Not that much for them to do there and the whining about being “bored” when they are waiting around a lot is real!
We stayed at AKL and having only buses to go anywhere was inconvenient for sure so I would stay on property but somewhere where you have options for transport.
We had 9 day passes, no park hoppers because the kids were so little that we started very early, had one dining reservation a day, usually lunch to give them a cool break. We then were able to feel refreshed and carry on for a few more hours. One family wrapped up their day at the latest by dinner time and those kids were done. Once those kids were back at the pool there was no way they wanted to hop anywhere else. You might want to consider that the little kids might want to be done their day with a pool swim and being at the hotel. We never regretted not having hoppers at all but that might have been due to the fact that transportation was a bigger issue for us. But the 2 and 4 year olds were really done once they got to the hotel.
You will have a wonderful trip but it’s very hard to anticipate how small children will react to things and in some parks there is very little for them to go on so there a lot of waiting around for them which can really be trying at times!
But you will enjoy and the last suggestion I would have is to do Genie+ in MK and HS for sure. I know it’s pricey but like my son in law said to me if it cuts down a 60 minute wait to 10-20 mins or even less it’s definitely worth it!
If you have any other questions I can help with let me know! Also make sure to do Typhoon Lagoon. Definitely worth it.