Aside from a taxi or unlicensed cab (Uber or Lyft), there are three other options for one-way transportation from the airport to the Disney Springs Hotels.
Shared Red Shuttle: Mears Transportation operates shared ride shuttles. Mears is the company that runs Disney's Magical Express service. They've been a Disney partner for decades, so they are reputable. Shared ride shuttles cost $24 for adults and $19 for children. For you party, that's $105. Shared ride shuttles may make stops prior to arriving at you hotel.
Private Vehicles: Mears also has private car service direct to your hotel form the airport. For a party of five, you need an SUV or van. One-way pricing is $98. (Obviously, that's the best option.)
Mears Transportation:
https://www.mearstransportation.com/
The third option is a little outside the box. You might want to price a one-way rental between the airport and Disney Springs. Sometimes you can get a deal around $20 and other times it's over $100. It really just depends upon your dates. You will need to get gas prior to returning the car, but that's pretty easy as there's a gas station across from Disney Springs. You shouldn't need to pay for parking if you're just dropping off your family/luggage before returning the car.
The following rental car companies have locations at the various Disney Springs Hotels. All locations are within walking distance of all hotels.
- Avis: Hilton Lake Buena Vista
- Alamo/National: Hilton Buena Vista Palace
- Dollar: Wyndham Lake Buena Vista
- Hertz: Holiday Inn Disney Springs
- Enterprise: B Resort and Spa
- Budget: DoubleTree Suites
Now for moving to your Disney Resort, the easiest method will probably be via taxi. Maybe have one person accompany the luggage in a taxi. The Bell Services folks will be able to assist with luggage at both hotels. Whoever goes with the luggage can use Disney transportation to meet the rest of your party at whatever theme park you choose.
When you say Disney Springs hotel, presumably you mean an off-site resort, correct?
FYI: There are seven hotels next to Disney Springs that are located on Disney property but owned and operated by third-party companies. Collectively, they are known as the Disney Springs Hotels. Because they are on Disney property, most people do not consider them to be "off-site" resorts.
https://disneyspringshotels.com/