OK, deep breath, call the school on Monday, find out where you were on the list, how high your DD would be on the wait list. It could be there will be movement in the list if you get on the ait list, my DS starts the september and so far, I have spoken to 3 different mums who are planning to privately educate but still applied for a state place (I do wonder why they bothered and didn't make the decision between state and private earlier). I know others who have been offered what are outstanding schools, but have/will move house before September so are wait listing other closer schools, so all in all, there will be lots of people moving around in this town before September.
However, none of that helps you if you haven't got yourself on the wait list!
Are there any other schools you could use - even if it involves using the breakfast club for one of your DCs? (I know there's just over a mile between 2 in our town, perfectly possible to drop one at the breakfast club at school A then take the other to school B. See if you can call the council and ask if you can go on those wait lists as well as the one you applied for. Remember, that solution doesn't need to be forever, schools are allowed to take an extra 2 places at KS2 (so 7), and people move house, I know someone who moved after the christmas of her DS's reception year when someone else left the area so a place became available at her 1st choice school. It might be your DD2 could move to your DD1's school, or you might have to consider moving DD1 to a school DD2 is at.
Granted, the faith school doesn't sound good for you, but you aren't going to get your prefered school so you need to start looking at other solutions. They can't just make a space for your DD2, so unless someone else declines, you can't get her in.
As others have said, you shouldn't decline the place without another offer on the table. If the catholic school is more than 2 miles from your house you might be offered free transport, would that help, even if it's just for a year. Can you go view the catholic school? Specify that your DD isn't catholic and ask about how they accomodate other faiths.