If my mother’s sister and my fathers brother have a have a daughter, how close will her DNA be to mine? Would we be as close as half siblings?
Yes, you are genetically indistinguishable from half-siblings (or an aunt). Regular first cousins share 12.5% of their DNA. As for double cousins, the cousin number is doubled. 12.5%*2=25%. That's exactly the same as half-siblings, aunts/uncles, nieces/nephews, grandparent or grandchild.
The expected match is around 1,750 cM with the low end of the range at 1,300-1,400 cM and the high end of the range at 2,100-2,200 cM.
According to PaternityUSA's sibling DNA test page, there is not much difference in the amount of DNA between half siblings & cousins, and so a sibling relational test is not a good choice for this situation. There are other more involved test such as a family reconstruction DNA test that may be able to give you the answers you need. You may be able to call them at perhaps they can direct you towards a test that would.