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?
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.
https://lmgtfy.com/?q=double+first+cousin+dna takes me to (first hit) https://genetics.thetech.org/ask-a-geneticist/double-cousins-share-one-quarter-their-dna, which looks like it answers your question.