Consider Mirena. Mirena plus oestrogen patches have been a bleed-free, side-effect-free godsend for me.
The problem comes that if a woman is progesten-sensitive, often she will bleed continuously even with Mirena. That was certainly my experience with Mirena and I tried it twice. And if she is menopausal or perimenopausal, it might not be possible to administer the drugs that stop that continual bleeding (I had them and they still didn't work although in my case I was using the device as a contraceptive). BUT, and this is a BIG but, what could work is if you have a gynae who specialises in menopausal women and who understands that this woman is progensten-sensitive and the side effect she experiences is continual bleeding. Then perhaps a Mirena can be trialled, in combo with a different form of HRT to control the hot flushes, but with the understanding that if the bleeding doesn't abate within a reasonable time frame, other options can be explored, not fobbed off for months and months with 'it will settle' because often times, in women who experience continual bleeding from progesten-based devices or pills, it won't. And again, of course, it has to be with a consenting patient.
Is there a chance, OP, that you can visit your GP and be referred to a gynae who specialises in menopause?
Queen, can you perhaps provide some links to doctors who might be able to help the OP? Some cases are more complex than others.
In my case, HRT worked to control my hot flushes and sweats, I did combine this with a lot of self-care, which I noticed even before I went on HRT helped somewhat (I don't drink or smoke but lost a stone and stepped up the exercise A LOT and that did have an effect).
But in someone who doesn't want bleeds, there needs to be options and treatment open to her, IMO.
I hated the Mirena, FWIW. It just made me bleed and bleed and bleed, even with drugs to stop it (all they did was turn it to brown sludge), and I also experienced a number of very negative side effects, but I was using it for contraceptive and in my 40s.
Just really wish there was some real help for menopausal and perimenopausal women experiencing negative effects that doesn't involve fobbing off or throwing up hands saying you have to suck it up.