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is it possible to clarify what the legal situation is, as it does make a difference.
If you sister is the legal power of attorney, then she has discretion to purchase gifts/ items or even give sums of money to people in your Mums life who would she would normally have done so for, obviously the expectation is that this would be done fairly and in proprotion to what your mum would historically of given. So theatre tickets etc don't sound completely unreasonable if thats in keeping with what your mum normally does.
With POA the 'attorney' has a legal duty to keep detailed records of how money has been spent and a lawyer (whoever helped to set ir up in the firstplace) will have to look at these accounts at intervals.
If no POA was set up, this probably means that your mum set up to have her finances (ie bank accounts etc) in joint accounts with your sister, if this is the case then there are really no safeguards in place. the banks won't be checking up unless someone asks them to.
If your sister (and I get the strong feeling from your OP that you suspect she is) is indeed 'skimming' money then she is comitting a criminal act and could face very stiff consequences. if your mum is in in a care home or similar (or even getting care at home) and someone is spending monies which the law would expect to be taken into account to pay these fees, then the Local County council would eventually get wind of this and may insist on the monies being reimbursed.
you basically have two options, you can either 'confront' your sister direct, maybe explaining that if she were inadvertently overspending on her mums behalf then behalf does she realise some of the consequences. Hopefully this might jolt her a bit. if you dont want to go down this road then you can make whats known as a 'vulnerable adults referral', you just ring your local police station, and say you want to anonymously raise a Vulnerable adults referral. The police are generally very tactful and dont go in 'all guns blazing' but will take thr time to ascertain what is really going on'.
I think your Dh is on very sticky legal and moral ground to state he is not going to repay any loan, that may also be seen as trying to hide a gift which could be counted towards the cost of her care.
Hope this helps