Not to offend anyone who loves/owns at Kidandi but it has refered to as Animal Kingdom Lodge Lite. I have stayed at both and would agree. The lobby is about a third of the size,, no quick services and a very small gift shop. I have many fond memories of breakfast outside Mara before hitting the parks at AKL. Unless it has changed, the pool is also themed better although Kidnadi has a pool play area for kids.
How much cooking are you honestly going to do when you on vacation? The great part of Disney is you can take your kids everywhere without hesitation. Every restaurant besides Victoria and Alberts. If your eating offsite, how are you getting there? That would be more of a hassle then its worth to me packing up the kids, driving to eat off site. Plus outside of the Dsiney bubble it is very touristy. Have you considered the dining plan? I would think it will be back by then.
Reconsider the split stay. I have done simular trips and it was the best decision. After 7-10 days you are going to have to do laundry. We always had a resort/slow day before our switch day. Kids went swimming, did laundry, repacked and hit the parks the next day and return from the parks to out new resort. Disney picks up your bag and delivers them to the new resort(unless that has changed post cover) The kids love it, its like a whole new vacation and let be honest the kids only care about a whole new pool!
If it were me I would split between the the Poly and AKL. Your on the monorail, with the kids ages you will be at MK probably the most. Stay away from grand it is completely overrated. Are you American? I ask only because my German relatives loved Wilderness because of the American West feeing it has and it is also a beautiful resort.
Another thought, for the price you are paying for rooms you could rent one hell of a vacation home. But that is whole other discussion!
Just to make your head spin at litlle more,lol, our favorite is Yacht and beach. We love having the boardwalk being able to walk/skyliner to Epcot and the studios and the pool there is the ultimate.