You do legally own half of the house, even if your name has never been on any of the documents - it's a marital asset, so it's 50/50 as the starting position, and nothing you've said reduces your share. That's the legal position.
The UC position is that they will disregard your share of the house for 6 months while it is being actively sold, but then you'll need to live off your share. If you give that up, they'll consider it an intentional deprivation of assets and treat you as if you still have it.
Presuming you are over 25, you'll get £393.45 for you, plus £333.33 for your first child and £287 for your second, so a total of £1013.78. There may be additional rates payable if you or your child have a disability and receive an appropriate disability benefit at a middle or higher rate; or if you've got ofsted-registered childcare costs for any of the children.
While you've got no housing costs, you'll be able to earn £673 a month before your UC is reduced, and £404 when you do have housing costs. Housing costs will be paid at your LHA rate, which you can find on your council website, and how many bedrooms you'll be entitled to will depend on your children's ages and genders.
CAB are not the most clued up about UC, unfortunately.