Investigators say the victim, a 46-year-old woman, was hit five times, twice in the arm and three times in her leg.
Police say her two children were sleeping on a mattress next to her bed, but were not injured.
A neighbor watched the gunman spray the home at close range.
"Four men were out milling around. One of them walked up to the front of the house, kicked the front door and opened fire. I ran back and grabbed my shotgun, worried they might come back but they didn't," neighbor Brian Abbott said.
The victim and her family asked that we not identify them by name.
The victim's husband explained that his family sleeps together in a front room when he's away for work as he was around 4:15 a.m. Sunday morning.
"I got up to see if my kids were okay, and that's when I got hit in the leg and arm," said the victim.
Police do not believe the woman and her children were the intended targets.
Some neighbors and family members suspect the men were looking for the previous residents or just had the wrong address.
Police say the four men drove away in a silver or gray four door Honda.
The family is scared, but grateful they survived, especially as the mother thinks about what could have been.
"Thank God they didn't hit my two kids. I'd rather take the hit then my two kids," the victim said.
Anyone with any information is asked to contact New Castle County Police at 302-395-8110 or call Crime Stoppers at 800-TIP-3333.