Is it required to buy a ticket to the museum just to sit in the restaurant?
My sister with her husband are going to the museum but I want to babysit their daughter.
I had a quick look at the van Gogh Museum website, found a link to the restaurant and it says
The café is open daily during museum opening hours and can only be accessed via the museum
From that I read that you can only visit the restaurant as a ticket holding visitor. I have not opened the floor plan pdf, you will find a link to it on this page, but the answer by @Zach Lipton indicates that the restaurants location makes crossing part of the museum needed.
As mentioned in the comments to the question, you could use the restaurant of one of the other museums on the square, like Stedelijk museum or Rijks museum (less suitable), both of which are open for public who do not have tickets, or if the weather is nice sit out in the square itself.
There are also several pub-like places on the square where you will be welcome with the child, if an escape for a sudden rain shower is needed. Or to sit part of the time with a glas of ranja (the local limonade for little children, orange taste, mixed with water) and whatever you like for yourself.
My vague memory of the layout is that the cafe is inside the ticketed area. The floor plan seems to indicate that this is the case as well, but I'm not absolutely certain.