If her name wasn't on the account the bank should have rejected the deposit. If the bank rejects your deposit the IRS will mail a check to the address on your return.
is the wrong a/c your MIL a/c (have her name on it)? if so she'll have to contact the Financial Institution or withdraw the money. The IRS will do nothing. now if your MIL's name is not on the account the refund should have been returned to the IRS which will issue a paper check. it will take a while for her to get it.
The IRS encourages banks to check the names on direct deposits, but the bank is not required to do so. Many banks do not check. If your mother-in-law's refund was deposited in someone else's bank account, she should contact the bank, explain the error, and ask the bank if they will help her recover the money. If the bank won't help, your mother-in-law will have to consult a lawyer.
Neither the IRS nor the bank is at fault. They followed your mother-in-law's instructions and deposited her refund in the account that she designated on her tax return.
See the following page on the IRS web site, particularly the third bullet under Scenario and the fourth (last) bullet under Solution.
@herminia_6_28 - The best approach is to talk to the Bank. They can't be willy nilly in crediting deposits to bank accounts. They have to have a risk managment approach to be sure the right money ends up in the right accounts. While the high speed approach with the millions of daily ACH transactions is the account number, they have to have some OTHER controls in place to ensure that money ends up in the correct account - because "stuff happens".
Having worked for one of the largest Banks in America, I know Banks have responsibility here. The bank may not be at fault for creating the misdirected deposit, but they certainly have responsiblity to have controls to mitigate the possibility of it occuring and controls to ensure that money ends up where it is supposed to. That control can include customers complaining about a mis-directed deposit.
So call the Bank. Use the word "complaint" frequently. Banks have very specific requirements from the OCC, their regulator, about how "complaints" are handled. Ask that your concern be escalated to a decision-maker as the front line employees will not understand the significance of the issue nor will they likely have access to the raw ACH transaction file that includes the name of the account holder that the money was to be credited to. Instist the Bank review the ACH transaction as they will see that the name on the ACH transaction does not match the name on the account the money was credited to. Since they have that data, they have responsibility (their controls) to make sure the deposit gets corrected.
good luck!
ps - as @rjs link indicates, the IRS takes no responsibility here, so contacting them isn't a good use of time in my view.