Actually, your situation may be rather complex. Here's some information to consider as you consult an SSA representative and your financial adviser or tax person. Mother should file for benefits at the latest by age 66, and father should file for benefits at the latest by age 70. No exceptions. Now to the options for the meantime.
First, let's say that the earnings reduction test does not affect mother and father in the year they turn age 66, but see below. To maximize retirement benefits over their lifetimes, most likely, they should both collect benefits as of January of that year. The permanent reduction in benefits is so small for collecting a few months early that they would be ahead in total money paid to them for many years to come. If an appointment is made in November, December, or January before they turn age 66, this will all be explained there. Next, they should get those numbers from SSA and bring them to a financial adviser or tax person to check on tax liability, then make a decision.
The January date is based upon the fact that the earnings reduction test typically does not affect retirees in the year they turn 66 and most can collect benefits throughout that year. Ultimately, this depends on three things. (1) The earlier in the year of the birth date, the more likely full benefits would be payable throughout the year. (2) The lower the income from work, the more likely full benefits would be payable. (3) The SSA appointment must be made before the end of January or they won't pay anyway.
As a general rule, a person applying for retirement must file on both their own earnings record and the spouse's record if the person can file on both. In other words, mother will file on her own record, and will file on father's record if he has filed (assuming her PIA is less than half of his as explained in my earlier comment above). You need not be concerned about having a choice here.
DELAYED RETIREMENT BENEFITS.
Despite all of the above, Delayed Retirement Credits (DRCs) are also an issue. I assume you want to suspend father's benefits for this. Comparing DRCs to age 66 benefits is very much like comparing reduced benefits to age 66 benefits. I am going to run an example assuming someone turns 66 in 1943 or later, but see here for the right numbers which will hover close to my example numbers.
Let's say father was born in 1943 or later, that his normal amount or PIA (see my comment above) is $2000, and that his DRC benefit is 24 percent more or $2480 at age 70.
If he takes benefits at age 66, he will receive $2000 per month for 48 months or $96,000 before age 70. He will be locked-in at this amount for good.
If he waits, he loses that $96,000 but gets $480 more per month after age 70. He starts out way behind. It takes time for him to recapture this lost 96k. The amount of time it takes may be calculated.
200 months = 96,000 initial loss / (2480 - 2000 monthly gain)
200 months is nearly 17 years. Add to this the initial 4 years of waiting. A person fitting my assumptions will wait nearly 21 years from age 66 to see so much as a dime of increased benefits for waiting! This is called the break even period. This is why I say over and over again, for most people, take benefits as early as possible.
DRCs transfer to widows. Now you have to gamble on how long they will live. If father waits until age 70 and both pass away within the 21 years from age 66, they lost the bet. If one or both survive, they start to see the $480 per month in aggregate additional benefits. Again, this is without considering taxes which may reduce that 21-year period.
I did all of this so that you will not go in assuming father's benefits will be suspended. That is a mistake many people often miss, even those well-schooled in finance and accounting.
SPOUSE WORKING FOR SPOUSE.
Here's another wrinkle for you that could affect collecting benefits in January. If income has been around or below $40,000 in recent years, you're done with this issue. However, a corporate officer or self-employed person may not be able to collect benefits or may only collect partial benefits until age 66 where earnings have been above $40,000 in recent years. This rule would apply to both parents. From here, it gets messy. I'll just add this: any period of suspended benefits in the early part of the year in which they turn 66 will be reviewed and permanent monthly benefit amounts will increase accordingly. Filing in January may still be beneficial even if some months of benefits are suspended.