Sounds highly illegal! I'd check your contract to see if they can make you work for no pay. Traveling outside of a normal commute is usually considered work time depending on where you are. Also making you pay for transportation to someplace so far is also usually problematic, again depending on local laws
YOU ARE NOT CRAZY!!!!!!!!!
Tell them you cannot go because not only can you not afford it, going without pay will endanger your health. Empasis on the health part
All that said too bad your dh can't get the day off so you can both spend the weekend there. imho that would be worth some out of pocket money. Nice hotel, no kids, sight seeing

or better yet tell M to long walk off short pier and take E for a girl's weekend in the car