Sorry I just saw this so this may be too late to be helpful. You are correct, there is a 60-day period in which you can receive a rollover distribution from a tax-qualified retirement plan and then deposit those funds with another plan without paying taxes and penalties on that.
The attorney you are working with who is the plan administrator is at fault here. As a plan fiduciary, he has a legal obligation to administer the plan in the interest of participants (you). If he made a mistake, gave you false or misleading information or made promises that he couldn't live up to and you acted in good faith, you may qualify for an automatic extension of the 60-day period. The automatic extension conditions are below my reply. If all of what I suggest below doesn't work, the plan administrator should work with you on the extension or should make you whole (the plan will carry error and omission insurance for this purpose) if you need to pay the penalties.
I think the safest bet is for you to put the money back in your old IRA or open a new IRA tomorrow, both of which are valid options for getting in under the 60-day window. Your current bank may offer an IRA that could ease the transfer. You can just dump it into a money market account short term. I know you're tied up tomorrow, but get on the phone when you have some waiting around time and get this done. Explain your situation and see what they can do to help you - it will be well worth it to not get hit with taxes and, if you are under age 59.5, the 10% early withdrawal penalty. You may need access to a printer and scanner or fax machine if you have to print forms, sign them and send them back (hopefully not needed but you never know). The clinic should have a business office that you can get access to while you're there. If you have a laptop that you can bring with you, scan in a copy of your license if you can before you go tomorrow so that if you have to transmit a copy of your ID, you already have a soft copy. This is why I'd go with your current bank, if they have an IRA, or your prior IRA. In both cases, you've already gone through the identification process required for anti-money-laundering requirements. Do everything you can to get this under the umbrella in a qualified retirement plan/IRA in under 60 days. You can worry about how to invest it for the long term when you do the rollover into the company retirement plan when it is ready to receive funds.
Here is a link to the self-certification process and model letter if you can't get this moved to an IRA in the next day. Given that you work for a law firm and they are the plan administrator, they should help you out with drafting and filing anything that you need to get this waived.
https://www.irs.gov/pub/irs-drop/rp-16-47.pdf
Good luck, both with this and your husband's appointment!
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The financial institution receives the funds on your behalf before the end of the 60-day rollover period.
You followed all of the procedures set by the financial institution for depositing the funds into an IRA or other eligible retirement plan within the 60-day rollover period (including giving instructions to deposit the funds into a plan or IRA).
The funds are not deposited into a plan or IRA within the 60-day rollover period solely because of an error on the part of the financial institution.
The funds are deposited into a plan or IRA within 1 year from the beginning of the 60-day rollover period.
It would have been a valid rollover if the financial institution had deposited the funds as instructed.
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