Please see below. When the unforeseen circumstance is not standard, the IRS still allows for special circumstance. They are citation from the Publication 523. https://www.irs.gov/publications/p523/ar02.html.
Under special facts and circumstances, "The home became significantly less suitable as a main home for you and your family for a specific reason." is one element which may fit in your situation. When the two children are infants, their activities and needs may be very different and unforeseeable from when they are learning to walk, climb, and run. So, the house could become unfit and even unsafe for them. Then, it is significantly less suitable as a main home. Then, you should be able to take partial exclusion.
Please continue to see below.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP
You may want to review all factors to make sure your circumstance fits or unfit all elements.
Showing facts and circumstances. If your circumstances do not match any of the standard requirements described above but based on facts and circumstances the primary reason for sale is work-related, health-related, or unforeseeable. Important factors are:
The situation causing the sale arose during the time you owned and used your property as your residence.
You sold your home not long after the situation arose.
You could not have reasonably anticipated the situation when you bought the home.
You began to experience significant financial difficulty maintaining the home.
The home became significantly less suitable as a main home for you and your family for a specific reason.