Simply, to get all the things your wife wants is likely not going to tow well with a half ton SUV. That's 6500-8500 pounds dry, or 7500-10k loaded with 950-1300 pounds of TW. No SUV after 2006 has a receiver limit over 1000 pounds and they all cannot be replaced/upgraded. So much for 9000+ tow ratings, at least for large families and RVs.
The practical limits for towing with half ton SUVs while carrying a larger family are payload and receiver rating. Most half tons have 1300-1500 pounds of payload. Subtract the weight of family and some things to occupy travel time and the rest can be used for trailer TW. Your children are little for now, even with child seats under 100 pounds each. You and wife, say it all adds up to 600 pounds. That would leave 700-900 pounds for TW, or somewhere around 4500-5500 pounds dry.
Our 3/4 ton Suburban would be perfect for you and allow a very nice TT up to 7k dry, maybe slightly more. But the last one was made in 2013 and you prefer Fords.
What works for towing an RV with 3-rows of seats? Full sized 1-ton vans. GM has some. Nissan NV3500 is better appointed.
Taking two vehicles is another option. Keep the Explorer and get a very cheap HD pickup, regular cab even. Could get for about $20k as dedicated tow vehicle and last 20 years!
