I don't know how much you earn Ben, but you can use these calculators to check if you might be able to get more help. Just remember that the results are based on both you and your wife being able to have benefits and your wife can't have all of these.
https://www.gov.uk/benefits-calculatorsi.e.
Tax Credits is a benefit and is nothing to do with taxes. This must be claimed in both names as it is benefit fraud to claim you are single when your are not. As a very rough guide, the cut-off for this benefit with one child, is a joint salary of about 26K, based on your previous tax year earnings.
Housing Benefit - you could claim for yourself and your child, but you must not take extra HB for your wife.
For these benefits, a two child limit has now been brought in following this recommendation from the MAC (Migration Advisory Committee).
Just to confuse things even more, the above benefits are 3 of the 6 income based benefits being replaced by a new, "one benefit" called Universal Credit. All income based benefit claimants of working age will end up on UC, if they qualify for it, and the 6 benefits UC replaces will end.
UC is much better for those that want to to work as the Tax Credit benefit worked against these people, but UC is not so good for those that don't want to work much. We are still split into two camps on the boards, on what all these roll-out rules are on claiming in a full service UC area v claiming in an area that isn't quite a full service UC area yet
If there is anything you think you might be able to claim and are not sure for your wife, come back and I'll see if I can help. It might be one I know the answer to.