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.