I would suggest early May over Feb if possible. By May "season" in Florida is over and many snow birds have gone home. In addition, spring break is over and schools are not yet out in most parts of the country so your likely to have less crowded parks. Feb can also, on occasion, bring a cold snap that might make your trip less enjoyable. Especially considering your traveling with young children. If you do travel here in Feb avoid President's week at all cost. It's insanely busy.
We are a family of five, Florida residents, who has experienced many on site and off site visits. It is my opinion that both offer positive and negatives for larger families. Since you're leaning towards an off site stay and have already mastered the fact that a successful off site stay is infinitely better with a car. I would recommend a condo or home rental over a traditional hotel with your families circumstances for this particular trip. Here is why. You have a baby and three small children. Space under one roof makes life so much easier. As a mother who traveled often when my three were under 5 I can attest to the fact that most family trips in that season of life were not what one typically thinks of when they think vacation. It was basically taking my full time Momma gig on the road. (The scenery was different, but the daily job requirements were still there and in many ways more difficult because our routine was not the same.) Anything I could do to make life easier while traveling with small kiddos made life much more enjoyable while traveling. Starting with sleep. No one is happy on vacation when you have an overtired small child. Having a separate room or rooms for the children to sleep in always helped. As did a full kitchen because every meal in restaurants with littles is not always enjoyable. Being able to have a stock of their favorite snacks and easy quick meals in a full kitchen helped tremendously. We still did some meals out, but not all meals. The in-unit washer and dryer helped too. No need to come home to piles of laundry after vacation and we could pack less to take.
On site Disney offers suites and DVC units. Or you can rent DVC privately, but typically you may not cancel with private DVC rentals. Many people were burned by this when Covid hit. Regardless, even with having to pay for parking at the resorts off site is bound to be more affordable.
I would suggest you do your homework and stay in a condo rental close to the parks. Bonnet Creek is as close as many onsite resorts. Windsor Hills is pretty close as well, but depending on which Disney Park your going to would be about a 10-20 minute drive. In addition, Windsor Hills is just off 192 which offers tons of dining and shopping. We have rented from several Windsor Hills owners ,but when traveling with young children I prefer mickeymousehomes.com. They are a tad more expensive, but their units are great when you have young children.
If your budget allows, I would do more days in the parks then 4. Perhaps some days only for a few hours. Go at the children's pace. Your about to see WDW though your children's eyes and I promise you it's worth every ounce of planning and restructuring on the fly because these memories are priceless.
Enjoy you vacation.
If we stay for 7-10 days, is 4 park days enough, just to see the different parks, and use the rest of the days for R&R at the hotel, or go to beach maybe? Or try to go to Disney every day? Lots of questions! 
