I was wondering if she has some kind of mental issues really.
That's a very strange lie to tell, and a mad thing to do at that time of night.
My PIL's rang us once, MIL in a terrible panic, to say that FIL was very ill and needed to go to hospital. They are both diabetic and she was saying FIL couldn't walk unaided and kept passing out. She kept ranting about diabetic coma's and saying that they couldn't get an ambulance to come out. This was about 6:30am and DH shot out of bed and round to their house to drive them.
As they got to the hospital, SIL was arriving from work to meet them as they had called her too. FIL was taken to be examined while DH and SIL contacted their other two brothers and MIL's brother and sister in law to let them know what was going on.
FIL had a diarrhoea and sickness bug and the doctor was not happy with him for going to A&E because of it.
Later on MIL confessed to SIL that she had thought she wouldn't get to see us that weekend and had been hoping we would all come to the hospital (so me waking LO and dragging him off to A&E) if we thought FIL was seriously ill and she was very upset that we didn't fall for her manipulative game care enough to go.
Your SIL sounds the same. She knew she was in the wrong but she created a drama to get what she wanted from your DH and is now in some kind of sulky strop because he didn't give into her once he found out what she was playing at.
YANBU.