Whether you can claim them comes down to whether you provided over half their support. Without knowing whether the 104 is per child or how she and the kids are able to cover their non rent expenses it's hard to guess the answer to that, but it's probably at least a close call. Unless you are also providing lots of food or other monetary support.
But: You certainly do NOT have to pay tax on 650*12 of income. You DO have to report it as rental income but if you do your tax return as though you have rental income you get lots of deductions from that: their share of utilities, heating costs, property tax, property insurance, garbage pick-up,snowplowing, etc. Plus some depreciation on your house. It's a bit more complicated and requires a bit more expensive version of the software but it's likely to save you a lot of tax by reducing the amount of the 650 which actually gets taxed.