The parking brake has no hydraulic circuit and therefore has not enough mechanical advantage or leverage to be an effective brake while you are moving. It is also a drum brake and not designed to act as a dynamic brake - you will notice if you drive with the brake on for long it needs to be adjusted to take the shoe wear into account.
Bottom line is the emergency brake cannot be counted on to get you to the dealer.
Sounds to me like the hoses are weeping that go to the calipers, or the calipers are really shot. Replacing either of these is pretty straightforward. Good luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)