Car crash insurance company pays us(children) to take total care of my paralyzed mother as the result of a car accident. Do we have to pay claim or pay taxes on this money?
Yes, it must be reported as income and income taxes must be paid.
The income gets reported as miscellaneous income, currently line 21 on the 1040 form.
But you do not have to pay self employment tax, and your mother does not have to pay payroll tax as if you had a business providing this service to other people.
A similar scenario (but with a spouse) is described in Q and A1 on this publication from the IRS:
Q 1: Must a taxpayer pay self-employment tax on the income she received from an insurance company to care for her spouse who was injured in an accident and permanently disabled? The taxpayer is caring for her spouse in their home in an effort to avoid moving him to a nursing facility...
A 1: No, the taxpayer does not owe self-employment tax on amounts reported on the 1099-MISC she received from the insurance company if she is not engaged in a trade or business of providing care giving services, as appears to be the case in this situation. The taxpayer must report the full amount of the payment on line 21, Other Income, of Form 1040 or 1040-SR.
I am sorry about your mother and wish you the best.