"Can I just do the lump sum and send 1099 to my siblings for their portions?"
No. The IRA belongs to you only (as beneficiary of the original owner) and all income/withdrawals/distributions are taxable to you alone. If you send money to someone else, that is a gift, and must be reported on form 709 if the amount is more than $17,000 per person per year. (I suggest you send the net amount after taxes, since you will have to pay the taxes.)
"Can I roll it over"
You can do a rollover to an IRA with a different bank or broker, if you don't like the current bank, but the account must always be kept separate as an inherited IRA. You can never combine inherited IRA funds with your own IRA funds in your situation. If you have compensation from working, you may be able to use the withdrawn funds to make a contribution to your own IRA, but that is subject to all the usual contribution rules and is not a rollover. You must withdraw the money from the inherited IRA and pay the tax, then the money is just your money in the bank and you can do whatever you want with it subject to any normal rules.
"and pull out a specific amount each year (to avoid the higher tax bracket)"
That's entirely between you and your siblings. For an inherited IRA where the beneficiary is "non-qualified" (that's you), you must follow the 10 year rule. That means that you must withdraw the account down to zero by the end of the 10th year after the date the original owner died, and if the original owner was past their beginning year for RMDs, you must also take an RMD each year until the last year or the money is all withdrawn. (You can always withdraw more than the required minimum amount, but you must withdraw at least the minimum amount.)
How fast you withdraw the money, and how fast you give it to your siblings, is entirely between you and them. Just remember the money is always taxable to you alone, and you must withdraw all the money and close out the account in 10 years or less.
