Housing Benefits after 1st baby born

My wife has got ILR and I have spouse visa. Both me and wife do job but right now my wife is on maternity leave and I work as a self employed. We live with our cousin who is also married and have two kids.Tenancy agreement is in my cousin and his wife name.
We live in 2 bedroom house and share the rent.Recently my baby was born and someone advised us to claim housing benefits and other child related benefits.

My concern is that when we will apply for housing benefit so shall I show that I live with my wife also? And 2nd after claiming these benefits will it effect on my extension application after 2/3 years?

For housing benefit, all people living in the property will have to disclose their details and income requirements as you are related.

A 2 bedroom property with 4 adults and 3 children might be a problem, especially for spouse visa extension.

What if I dont show myself that I live with my wife? or what you suggest? whats the best way to get housing benefit?

What if I dont show myself that I live with my wife?

That would be benefit fraud and if she states that she is single in ANY benefit paperwork when she is not, when HO check the benefits records, they will see she has declared herself as single and your visa will be in jeopardy.

How much rent do you pay for the one room?

How much do you think your wife will qualify for in housing benefits?

I pay £600 right now for 1 bedroom and I am not sure how much she will get. Please help me I dont want to be a defaulter.

If you are renting one room in someone elses' house, you would be considered a lodger and the housing benefit for that arrangement is less than if you and your wife rented a property on your own.

Whatever you do, she must declare you if she claims housing benefits and your and her income will be used to work out IF she is entitled to anything.