The twins want to buy ice-cream. Their mother did not allow them to.

If the sentences are joined, it will be...

The twins want to buy ice-cream but their mother did not allow them.

Qn: Do i need to add 'to' at the end of the sentence?

No, it's not required.

Yes, it is one of the possibilities. But you have to make little changes to your sentence first:
The twins want(ed) to buy ice-cream but their mother did not allow them (to do so).
(to buy them).