There is specific information which the 2006 TUPE regulations require to be divulged from the outgoing to the incoming employer which you'll be aware of (length of service, holiday entitlement/holiday taken, pay rate and any disciplinary or grievance procedures outstanding) and it's not unreasonable to look to have any of these subjects verified. Some companies use outgoing TUPE to either dispose of employees they don't like very much or to put a spoke in the wheel of the incoming employer (a pay raise two weeks before transfer is related to the transfer so would not confer an obligation) and your due diligence can ensure that you have a true picture of the liability you're taking on.
I've mentioned this in previous posts, but a contract of employment is a relationship term and arises when you take someone on - it's NOT the terms and conditions of employment which the Employment Rights Act 1996 requires to be issued to employees and there is no reason that I can see which would require this document to be produced save where a dispute as to the veracity of the information provided is in doubt. Even then, you'd be looking for single documents rather than terms and conditions which would normally be the head of a paper trail including staff handbooks, employment policies, company procedures and so on so I'm not certain as to the thinking behind the solicitation of this document though I'll be happy to help further if you like.
If I understand your second question correctly, the contract is for your sister's office and the answer to whether she can dismiss the employee by terminating the contract is, legally at least, no. She could fudge by stating that she wants to cancel the cleaning(or reduce to two hours a week) to the current supplier since her 'own staff' are going to take on additional cleaning duties shared among them which would make the position redundant and if the cleaner hasn't been working for more than two years then there will be no redundancy payable but I'm not sure whether that works in her circumstances. I'd be happy to clarify with more details.
If you're looking to terminate the contract and you're in the London or Midlands area, I'd be happy to add 5 hours a week to my client list - I'd say about 15% of my contracts are in this range and I love them. When TUPE hands me a bad employee, I always assume that they've been badly managed and four weeks post transfer results in either a better employee or someone dismissed for poor performance. I recognise it's horses for courses, incidentally, and that's not intended as a critical comment on your own philosophy - running a business is like having kids. We mostly do it well but we all do it differently.
EDIT: I just reviewed this post and noticed that your question is whether your sister (the client) can request a copy of the contract/t&cons. The answer to that is yes but that there are a whole number of reasons why the company could legitimately refuse the request. There are exceptions - one company on our list has requested that the employee pay rate is at London Living Wage rates and they have contractual right to see evidence of this as required.