You need an attorney - perhaps to force her to move forward with the probate. Technically if the will controls the real estate and the will gives the house to you, your interest in the house vests upon Mom's death. That said, it is the executor's job to protect the estate assets and safeguard them. Now, she is not the executor yet because she has only been nominated, not appointed by the probate court - that is why the will has to be presented for probate. Most of the expenses you mention are costs of the estate (probate estate - those assets owned by Mom alone at her death) so you are entitled to reimbursement for out of pocket costs to the extent there is any cash for that. Both sides have legal rights and obligations and non-compliant family members often don't change on their own - sometimes they need to be prodded.
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Mr. Zelinger is spot on. You absolutely need to retain an attorney to advise you on how to proceed, if for no other reason than that it sounds like you'll end up being on the losing end of this deal for a long, long time if you don't force your sister to probate the estate and fulfill the fiduciary duties she has as presumptive executrix of the estate. In other words, paying an attorney to represent you now and get this resolved may end up being a lot cheaper than letting things go as they are now and just hoping that your sister will eventually turn the house over to you.
Also, if she continues to abuse her apparent position and doesn't probate the will, then you may have to contest her appointment as executrix in the surrogate's court, and that will definitely require an attorney.
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From the facts you give, your sister has no motivation to probate the will. She's not getting anything under the will, and she can't even collect executor commissions on the house if it was specifically left to you. In New York an executor cannot collect commissions on a "specific bequest", unless the specific bequest must be sold to pay any debts your mother owed at death or expenses of administering the estate. By any chance, are you the successor executor named in the Will? If so, have your sister renounce and probate the will yourself. If she won't renounce, and there are no other successor executors named, you should still go ahead and probate the will yourself. Your sister has no reason to want to do it, and you do, so it's going to be up to you to probate the will.