The first one is better. For the second one it would sound better if you said, “I help my mother while/when she is doing the housework.” A simpler way to say this is “I help my mother with the housework”

This is why English is stupid. The first is correct, but in spoken English the second is probably more common. You could also say "I help my mother with the housework." To understand why I say that, the second sentence will be understood by a listener from context and intonation, and it's lazy. So we talk that way. When written, I'm asking myself if you're saying that you help your mother at the same time as you are also doing some unrelated housework. The second sentence isn't as clear in meaning, and I feel like there could be a "while" in there to make it say "I help my mother while doing the housework." Hope this helps.

I help my mother doing the homework.

Help some one to do something