Nanny share - gift for other kid?

We nanny share twice a week with another family and have been for 2 months. We don’t exactly see eye to eye with the other family (they made us deal with finding childcare for a whole week because their kid was sick - ours was not - and the nanny share is at their house so they felt they “get her”, then the nanny got sick and we had to deal with finding care again the following week!). We have unresolved disagreements and basically are polite to one another and that’s it. Is it expected I get their kid a Christmas gift though?

Let me clarify the kid is a baby (8 months old) and wouldn’t know if we didn’t get them anything! My child is also a baby.