It might be easier to understand this by talking about non-probate assets. A non-probate asset is one that is transferred outside the will or intestate succession (the laws that govern how property passes when there is no will). So, typically, non-probate assets are those that are accompanied by a beneficiary designation form that allow a person to designate who shall receive the property upon death e.g. life insurance policies, Retirement Accounts, possibly CDs, etc. Note that all property can be made into non-probate property by sticking it in a trust that governs how that property is to be distributed upon death. This is typically done in a Revocable Living Trust. In your case, it looks like non-probate assets might be the Life Insurance Policies and possibly the CDs.
Disclaimer: This answer does not create an attorney-client relationship. The answer should not be relied upon as it does not comprise legal advice. Each situation is fact sensitive and one or two facts could change how the law applies to that situation. To fully understand how the law applies to your situation a thorough analysis.
Probate assets are those assets that can only be transferred with the intervention of the court. The primary purpose of probate is to transfer title to assets. If the deceased person took advantage of a trust arrangement, whether formal or informal, during her lifetime, there is no need for court involvement after her death.
ITF stands for "in trust for," and is a type of informal trust. Therefore, if the beneficiaries are living at the death of the person who established the account, there is no need for a probate. Title passes as a matter of law. The same is true for any account that allows for named beneficiaries or designates beneficiaries as POD ("payable on death") or TOD ("transfer on death").
Most joint accounts, whether the person contributed to the account or not, will pass to the surviving account holder by operation of law and is not subject to probate, either. However, the courts in some states have ruled that such accounts, if it can be shown that the joint owner was placed there solely as an accomodation, are an exception to the rule and really belong to the estate of the deceased. Once the court has so ruled, the account would be part of the probate estate, as well. If the account is large enough to pay for lengthy litigation and you have such rulings in your state, it may be worth pursuing.
Most states have a provision for the expedited probate of small estates. If the car and the co-op apartment are the only assets subject to probate and their combined value is below the statutory minimum the probate process is relatively brief and inexpensive. These statutory minimums vary widely from state to state, so you will have to do some research or find an attorney in your mother-in-law's state to assist you in this matter, as well.
Disclaimer: This answer does not create an attorney-client relationship. The answer should not be relied upon as it does not comprise legal advice. Each situation is fact sensitive and one or two facts could change how the law applies to that situation. To fully understand how the law applies to your situation a thorough analysis by an attorney licensed in your state who is familiar with this area of law may be necessary.