Welcome!
Hello, Liz, and a warm welcome to TP. I hope you will find it a source of information, advice, and support, as I've done over the past year.
I'm very sorry to hear about your challenging situation. Being a caregiver is never easy and double duty must be very difficult and tiring for you.
I think it's very reasonable for you to have found a respite placement for your mother. I'm sure it's not what anyone's first choice would be, but please do try to remember that your mother is being looked after and cared for, in respite.
I'm especially sorry to hear that your mother is not settling well into respite. While it's not uncommon, it definitely does NOT make things any easier for anybody. It sounds as though she has only been there for a couple of days, which of course isn't nearly enough time to settle. As another only child who has been there with moving a difficult mother into care, please don't berate yourself if you do not visit your mother for a day or two or three. You can keep in touch with the staff via phone, to get updates on how she is doing. If there is an emergency, they will contact you. The point of respite, after all, is to allow you to have time for things you need and want to do, not to place the person in respite and then spend 24 hours a day with them! As you are a carer for your husband, I am sure you have your hands full.
Dementia is very challenging. No one here will judge you if it turns out you are not suited, or able, to provide 24/7 care for your mother indefinitely by yourself. Some people do, and some people don't, and nobody can be a sole carer, without help, indefinitely, and not suffer from it. If and when a care home becomes necessary, it does. I am not sure how you could possibly manage to care for your husband after his surgery and your mother at the same time with no assistance. I wonder if you might consider a respite placement for your mother, until your husband has recovered somewhat from his op.
Others here, in the UK, can give you better advice about how to access help, such as day care, carers cafes, lunch clubs, in-home carers, attendance allowance, and so forth. I would encourage you to reach out for help and support for both your mother, and yourself.
I can also tell you that you're definitely not the only, only child on these boards. There are a number of us here and we know what it's like, to have to do this alone.
I'm sorry I don't have better advice, but did want to welcome you and respond. Best wishes to you and your family.