I hate to advocate welfare and all, and I know none of us enjoy going for it, but in a time of REAL need, I think it is more than acceptable to call on the government for help. I would have to say that you would almost definitely qualify for child care coverage in your state. They do it here in PA. I have never used it, but I have friends that have. Most people have it entirely paid for, and some pay tiny fees. My one friend paid $5 a week for her daughter to go to preschool/daycare full time at the YMCA. Check out the website for state assistance in NY and you should be able to see right off the bat if they offer child care coverage, and you could even see if you're eligible and probably even apply right there on the site.
Also even aside from that, search online specifically to find out if there is a "head start" program in your area. Your older daughter could do that, it's actually a really nice preschool program that is federally funded (free for you). It could be good for her, and provide as child care for you. My brother went to head start and loved it, he learned a ton too. Its a good program.
But seriously, look into some state assistance with that, if you are seriously hurting on money and you can prove it, they WILL cover what it costs to put your kids in daycare so that you can go to work!