My mother wants me to claim my sister and brother on my taxes this year because is was unemployed, is this legal and ok to do without getting in trouble with the IRS?

[Opus 17]

You can claim your siblings if you and they lived in the same household for at least half the year.  If their parent also lived with them in the same household more than half the year, the parent gets priority, but can allow you to claim them instead as long as you have more taxable income on your tax return than the parent does this year.  

If you didn't live in the same household more than half the year, you could still claim them as long as you provided more than half their financial support for the year, and if your mother has less than $10,350 of taxable income (including taxable unemployment if she received it).