When they say 4.5 miles to Disney they usually mean from the an entrance to Disney property. The MK is about 6 miles into Disney property, meaning you're about 10.5 miles from MK. The other parks will be a little closer.
I don't know anything about the Embassy Suites shuttle. However I have heard that often these hotels share shuttle service with other hotels so you could be making many stops before getting to the parks. Also, they tend to make a few runs in the am and a few in the pm. If you want to leave the park in the early afternoon for a rest, you are out of luck. If you miss the last bus, you are out of luck.
If you are staying off site then definitley drive to the parks. For MK you park at the TTC (just follow the signs to MK). From your parking space you will either walk or take a tram to the front of the TTC. From there you take either the monorail or a ferry to the MK. All other parks have parking lots near the entrance to the parks (although they also have parking trams). Just follow the signs to each park. Once you are on Disney property the Disney people move the traffic very well. Therte may be a little back up at the toll plazas.
I agree you should consider staying on site. I don't know what the Embassy Suites gives you besides some extra room. Do you plan on doing any cooking while on vacation? You could get 2 adjoining rooms at a Disney resort for extra space. Try two adjoining rooms at the All Stars or POP if money is tight. Check out
www.mousesavers.com for info on discounts at Disney resorts (and many other Disney discounts). It's a little early for discount codes for August but you can see what the historical rates have been with codes in years past.
You may find it is more affordable than you think. Plus, Disney transportation is much better than off site shuttles. From All Stars or POP buses run to each of the parks every 20 minutes or so (more often at peak times of the day). They run constantly all day long. From Swan/Dolphin you can walk or take a boat to Epcot or MGM, and take buses to MK or AK. Other resorts have differing methods of transportation, but they all run regularly all day long and are very convenient. Staying on site also makes it easier to go back to your resort for a mid day nap, which is very important for 2 toddlers.
Good luck planning.