Can a court order the other side to perform the contract?

Yes. Since the Specific Relief (Amendment) Act, 2018, specific performance is no longer discretionary: a court must order it unless a statutory bar applies, for example where the contract depends on personal qualifications, involves continuous duties the court cannot supervise, or is by its nature terminable, or where the party seeking it has not shown that it was ready and willing to perform its own part. A party facing a breach can also, after 30 days’ written notice, have the work done by someone else and recover the cost (section 20).