I'll just say it might make more sense just to take a taxi for simplicity, although four might be a tight fit depending on the taxi vehicle and the size/number of your luggage. The rules about San Francisco taxis is that they must accept any fare to any place in San Francisco, to San Francisco Airport, and to Oakland Airport. They can decline a fare to any other place outside of San Francisco.
One reason why I was thinking the Amtrak bus is that they can take lots of luggage while it might be cramped in a taxi - especially some of the smaller ones like the Prius taxis common in San Francisco. It could be fun to take the train, although it might cost as much total as the taxi ($14.50 for adults and half that for kids, minus a 10%
AAA discount if you're a member). On top of that it won't get you all the way to the airport - you'll need to take the BART connector or AC transit on top of that.
http://www.capitolcorridor.org/route_and_schedules/documents/Train_Schedule_10_26_2015.pdf
The bigger taxis will be Ford Escapes. The F-line can be really crowded, although BART will usually have some place where you can put your luggage - typically one spot generally reserved for bikes or wheelchairs.
This is estimating $83 (including tip) from the Sheraton Fishermans Wharf to Oakland Airport for a cab:
http://www.taxifarefinder.com/main....9,-122.413658&toCoord=37.7125689,-122.2197428
Assuming that you're paying the cash fare, you have two adults (you didn't specify that), and your kids are 5-12 (youth fare on all systems around here), it should cost the following:
MUNI (F-line to Embarcadero): $2.25x2 (adults) + $1x2 (kids) = $6.50.
BART (Embarcadero to Oakland Airport): $10.20x2 (adults) + $3.80x2 (kids) = $28.
or BART (Embarcadero to Coliseum): $4.20x2 + $1.55x2(kids) = $11.50.
plus AC Transit (route 71): $2.10x2 + $1.05x2 = $6.30.
So your entire ride is going to be $34.50 direct or $24.30 if you get off at the Coliseum BART and take AC Transit.
BART has discount tickets for kids, but they're kind of hard to find. The Clipper Card is easier for the kids (it's automated since you have to give date of birth), and there are two places in San Francisco where you can get one (at the bottom of this page). You will need proof of age, like a student ID, a passport, or a state ID:
https://www.clippercard.com/ClipperWeb/damagedCard.do
https://www.clippercard.com/ClipperWeb/discounts/youth.do
A lot of people just pay for adult fare on BART for kids because it's easier than trying to get a youth ticket or obtain a youth Clipper card. The system is automated and their ticket machines can't issue youth tickets. They can add value to youth Clipper cards though.
Here's the AC Transit 73 schedule:
http://www.actransit.org/maps/sched...ion_id=30&maps_line=73¤t_schedule=17106
Yeah - I get that this is confusing if you're never ridden on public transportation in the area. It's a lot of little fiefdoms since the everything is somewhat decentralized. In the Bay Area there are at least 14 different bus systems, 3 ferry operators, two light rail operators, two commuter rail operators, plus Amtrak. Just as a quick primer - "Clipper" is the interagency fare card used on most public transportation systems in the Bay Area (Amtrak doesn't take it though). Chicago has a system called "Ventra", while Southern California has a system called "TAP" - there could be something similar where you live. This kind of system stores a cash value that can be used on any system, as well as monthly passes and value that can only be used on a single system. BART typically uses magnetic strip fare tickets, although they also use Clipper. MUNI in San Francisco has many options. You could already have purchased a multi-day pass (a 7-day one comes with
CityPASS) so you might not need to pay cash fare if you're on your way to the airport.
So are you thoroughly confused yet? So my final recommendation is get a Clipper card for the kids to take advantage of the discount on BART and pay cash fares for the adults. Then just take MUNI to BART, then BART to the Coliseum station and straight to the airport so there's less to go wrong. You have a lot of options since there are several ways to get to a BART station from Fishermans Wharf. Google basically recommends this:
https://www.google.com/maps/dir/She...f03017460!2m2!1d-122.2197428!2d37.7125689!3e3