I hate to add to the family discord, but unless the person your mother is seeing at H&R Block is utterly incompetent and/or can't read (which I doubt is the case) they most certainly did NOT tell her that you would not need this information to pay taxes properly on your unemployment compensation. (Yes, I am calling this BS.)
Unemployment is clearly spelled out in plain English as one of the types of income upon which this tax is paid right in the form's instructions, under the definition of unearned income: https://www.irs.gov/instructions/i8615#idm[phone number removed]152
You need that information in order to properly prepare your return. However, if you can't get it, then yes estimate and the IRS can sort it out for you later.
As for the matter of dependent/not a dependent, the IRS will be happy to decide for the both of you if she is entitled to claim you or not. To get them involved, she claims you and you file stating you can't be claimed. One of you will have to file by mail in this battle, though, and you'll both get letters from the IRS explaining the rules urging the one of you who didn't follow them to file an amended return.
You could also check to see how the rules apply in your situation here: https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent
When that doesn't happen they start asking for the proof, and whoever can prove his or her case gets to keep their refund as filed and the other one gets a big bill with interest and penalties tacked on.
You need her income so that you can pay her higher tax rate on your unemployment. She's not "helping" you by giving it to you, aside from helping you to comply with the law. Show her the form, and its instructions and ask her what you need. If you are, in fact, qualified to be her dependent she doesn't need you to "let" her claim you and if you're not qualified she can't decide to just do it anyway.
As an aside, if you wait a week or so until the exemption for some of the unemployment compensation that passed last week is written into the software, you might save some money and frustration.
