How to get from Santa Maria Novella train station to rental?

There will be plenty of taxis outside the station so no worries about the wait
Make sure you go to the official taxi rank

The taxi will get you as close to your address as possible
Most of the historical center is pedestrianized
The cost should be about 10-15 euros

I am not sure if you need 2 taxis for 4 plus luggage-hopefully you are traveling light-one bag per person-but even 2 taxis won’t break the bank
There might be a van at the taxi rank
If you have to split up put one adult and one kid in each taxi

Have your address on a slip of paper to hand the driver
Taxis are required by law to take credit cards
Make sure their POS is “working” or just plan on paying with cash.

I assume you mean a rental car?
You have no need of a car in Florence-you can’t drive or park anywhere in the center

If your landlord means a private driver? That 100 euros is highway robbery

If you want to try to walk the route just google map Firenze Santa Maria Novella to Museo Nazionale del Bargello to see the route and distance. Keep in mind the weather will be HOT so you might want to consider a taxi. Google Maps for me indicates 18 minutes on foot.

I'd opt for the taxi. Walking with wheeled luggage isn't all that easy in Florence. Some sidewalks are very narrow, even along major streets, some in poor repair (uneven paving, potholes). And there are lots of crowds. There may even be a pickpocket or two.

Go in front of the station to the taxi stand. Ask the taxi steward you need a taxi (guy with yellow vest in image below) for a family of 4. Four passengers with luggage is not a lot, as many cabs are large station wagons or minivans.
The taxi steward will point you to the cab for you (there will be many queued up). Board the taxi after giving the driver your luggage for the trunk. Board the cab.
The charge will be shown on the meter. The distance is less than 3 km. The charge per km is initially about 1.10€ per km for the first tier, then it almost doubles in the second tier, but your distance is too short to reach the second tier, therefore your charge will be around 3€, unless there is a traffic snarl. To that amount you need to add 3.80€ for the initial flag down charge (or 6.10€ if on a Sunday or holiday). There is also a 1.20€ charge for each bag. The minimum charge must be in any case 5.80€ (or 8.10€ on Sundays or holidays), which you will certainly pass.
Assuming you arrive on a weekday (Mon-Sat) and not at night (there is extra cost from 10pm to 6am) and you have 5 cases, you should pay about 13€, maybe less, for the ride. If on Sunday about 3€ more.
If your AirBnB host has quoted you 100€ he’s planning to make a lot of money off you. I wouldn’t trust him even for the AirBnB rental. 120€ is the rate for going to the Pisa airport from Florence, which is over 80km away (50 miles). That is ridiculous. For 100€ I want one separate cab for each member of the family with a tour of the city center included.

https://images.app.goo.gl/UAiwGvUPcU5VS4Hj9

We recently trekked from the train station to our airbnb near the Duomo. It took about 15 minutes to walk. The streets are narrow, so I find it easier to walk on the street close to the curb. Note that most airbnbs and hotels don't allow check in until 3pm. What time do you arrive into Florence?

We arrived in Florence and all is well!

Roberto and Christine were right on. The only thing I would add is that the we ended up where we "thought" was out front of Santa Maria Novella and saw taxis coming up but no taxi stand or taxi director. I finally went up to one taxi driver and he told me to go to the other side of the station were people were cueing up for taxis. We didn't see a director, per se, but taxi drivers were seeing who needed a ride and grabbed us and fit all four and our four bags easily into a station wagon and drove us -- and experience in and of itself!-- to our luggage storage, which we found and booked online at a location our AirBnB (so it was easy to grab and walk around the corner when it was time for check in).

Dropped our stuff, had a light lunch at the cafe nearby and took off exploring. We had a yummy dinner at a restaurant recommended by our rental host (the parmesan truffle pasta was to die for!) and walked to the top of the Duomo cupola at the last reservation (6:45 pm) which was the only slot available when I finally booked a week or two ago --- but ended up being a wonderful time to do it! I'd highly recommend it!