Our family (husband and wife both age 45, son age 10, daughter age 8) is interested in traveling to India in late-december/early-January 2019 [moderator edit to remove commercial link]. We recognize this is possibly the worst time to visit India given the heat, but that would be the only time our children have sufficient time off from school for a trip.
We would like to travel for approximately two weeks, inclusive of international flights (roughly ten days in India). We'd like to see the usual tourist sites in Delhi, Agra, Jaipur as well as spending a few days in one of the national parks in the hopes of catching a glimpse of a tiger.
Main question: Are we insane to consider traveling in late December/early January, especially with children? Will the heat just be too stifling to enjoy sight-seeing?
Thanks in advance!

heat in late december/early january????

Heat is not an issue in that time frame, it's actually pleasant/cool at that time in that region. Heat is more of an issue in the late spring. The bigger challenge you will encounter is flight scheduling and cost, because, as you noted, Christmas break is when kids have time off from school so that's peak time when lots of people will travel to India, whether for tourism or family visits.

As has been mentioned, the heat won't be a problem. It will likely even be cool enough to need a jacket in the evenings. Fog is also a consideration during Dec/Jan when flights and trains in Delhi/Agra can be delayed.

If you can get over the often insane prices of flying to India during the Christmas season, it is a great time to visit.

it will be much cooler than that....the temperature is likely to be in the mid-low teens during the day & in the single digits during the night....i remember the temperature going down to 0 �c a couple of years ago in the first week of january....

Thank You So Much All, Highly Appreciated

why don't you include GOA in your list? its best place, you must visit GOA. Just think on it.

BTW till Feb end its almost winter season in India.

goa is not really an attraction for people coming to india....there are far better places outside india if you just want to visit the beach....

Yes that's true.