I work for the DWP. Yes you can.
You make a joint claim, but you would be expected to look for hours during school time, or when husband can look after them when his work finishes for the day.
You can still get UC, while both working FT, or mixed hours, compressed hours etc. Would need to be over 18 hours.
UC will not accept you wanting to be a SAHM. Hubby and I both work full-time and receive UC. He works in IT for 40 hours a week, I work compressed 30 hours over 3 days. The other 4 are for homeschooling my eldest.
If you dislike UC rules and don't want to look for work, then close the claim. However, I am curious why you aren't already getting child tax credits, working tax credits, housing benefit, council tax discount, and child benefit? Did you never apply?
You only trigger a claim to UC if you move and there's a change to Housing Benefit and Child Tax credits.