I have done this and they have been requested to provide proof that this was something that I received which they have not done.
There is no "proof" that you received it ($3700) because you didn't receive it. It was paid to the housing company. It has nothing to do with your claim on either of the coverages.
However, I do not see how this could possibly have been coded as Personal Property "as the cost was an expense that was incurred as a reasonable increase in my living expense necessary to maintain our normal standard of living while we lived elsewhere". This is the definition under the Coverage -E of the policy additional living expense This is not personal property owned or used by any insured.
Believe me, it does my heart good to see that you are actually reading your policy but your policy provisions have nothing to do with the $3700.
If it was added to your personal property loss calculations BY MISTAKE and then backed out, you haven't lost anything because you weren't entitled to it in the first place.
If you are thinking that the company is taking $3700 away from you, that is not the case because it was never part of your claim in the first place.
For example if your bona fide personal property loss was $50,000 (your actual figures may differ) and somewhere in the adjuster's claim file it says $53,700 BY MISTAKE, and the $3700 is backed out to correct the ERROR, your bona fide claim is still $50,000.
I have submitted to them a number of food bills, hotel bills and gas bills that occurred prior to the rental that they had advised they would cover does that come out of my Personal Property coverage too or from the Additional Living Expense coverage?
Those bills are covered under the Additional Living Expenses part. But notice the word "additional." The hotel bills would be in addition to your normal living expenses but the gas and food receipts would have to be adjusted to determine the additional amounts above your normal living expenses.
For example, if you spent $500 per week on food after the fire because you couldn't do normal grocery shopping and cooking you would have to subtract your normal weekly grocery bill and you'd be paid the difference. But if you were put into an apartment for a few months and could shop and cook normally you might not be entitled to any reimbursement for groceries. Same goes for gasoline purchases.