Short answer
Your very good question has two parts, and the second part is easiest to answer:
The creature cannot completely avoid dancing, as it begins dancing on the caster's action, and can only resist as an action on its own turn.
The question about movement and dancing on its turn seems chicken and egg, but I think the most natural reading of the spell is that all movement is exhausted on dancing, but the creature can make another action, either an attack or a saving throw to break free.
I argue this on two counts:
- the strongly-worded nature of the dancing rule
- the order of the rules as given within the spell
Ultimately however, this point is moot, and up to your DM's judgement.
The strongly-worded rule on dancing
I argue this on the basis of the strong wording of the statement about the dancing:
A dancing creature must use all its movement to dance...
This is the only use of must in the spell description, and the use of "all" makes the statement all the stronger. As the creature is dancing just before its turn, it is reasonable to assume it is a "dancing creature" as its turn begins, so it must use all its movement to dance.
The order of the rules in the spell description
The above strongly-worded statement comes before the action options:
...and has disadvantage on Dexterity saving throws and attack rolls.
The text about the possible saving throw comes at the end of the spell description, which suggests it is an alternative to the attack action, and so that like this action it can only be used once the creature's movement has been exhausted by dancing.
Your DM might not agree
I am aware there are some holes in my reasoning, and if your DM is not convinced then it, as so much else in 5e, is up to his or her judgement.