During the process of looking for our new house, we have decided to move to stay with our mom for a while until we get one. I wonder if staying with a person who is disable and cliams benefit from DSS will affect my wife's second visa. Currently, she holds settlement visa (spouse) which will be expired in 22 months.

No, it doesn't matter what benefits your mother receives, it is your and your wife's income that matters. You may need to demonstrate, though, that your mother's place is big enough to house you all. However, you might have your own pad by then.

Scouse.