"Everyone is being very sympathetic to Eva's situation," a source tells PEOPLE. "Work has to go on – but the whole set is very protective of Eva."
Adds the source: "Everyone tried to make sure yesterday that filming went as smoothly as possible."
According to a friend of the actress, she's "devastated" after discovering Parker had been carrying on a text message relationship for months with Erin Barry, wife of his former teammate Brent Barry.
"She is simply heartbroken," the friend tells PEOPLE. "She really wishes Tony the best. She just wants this whole situation to be as peaceful as it can be under the circumstances. He's a good person at heart, and she wants the best for him."
Helping her through the ordeal: a solid support system, including some of her Desperate Housewives costars.
"She has a group of girlfriends she's very close to that are helping her," Longoria's friend says. "She's also very close to her family. And the cast of Desperate Housewives have been wonderful, especially Marcia [Cross] and Felicity [Huffman], [who] are there for her through this."