The dog crawled . . . . . . . . the table with its tail . . . . . . . . its legs.

We use 'under' to talk about something that is below or lower than something else. First blank will take 'under'. The most common use of 'between' is when something is in the middle of two things or two groups of things. It is sometimes used in the phrase in between. Second blank will take 'between'.