visas: my passport has just been changed to married name, but the IDL tag is on my maiden name … I have to travel soon

My passport has just been changed to married name, but the IDL tag is on my maiden passport …
We are booked to travel on December 18th.

I currently live in the United Kingdom with an indefinite visa for permission to stay.
It's in my passport with my maiden name.
I applied for British citizenship and the United Kingdom passport office told me that I had to change my Aus passport by my married name BEFORE they issued my citizenship and my UK passport. Otherwise, I would have to have them in my maiden name. not be able to change it later (why the hell, I do not know, since I could surely have sent that passport with a marriage certificate and get a new one, but the lady told me no). I also told her I was traveling and she told me to make sure I took my marriage certificate and that it was okay.
Years ago, I booked the appointment in London to get my new passport and the wait was 4 weeks, I just came back.
Anyway, while I was there while I was cutting my passport with a visa, he told me to check with the local office in the UK when I travel to Christmas!
I have been waiting in the home office for more than 2 hours without an answer, but I have been searching on Google, only to find that if my name has changed, I must replace my visa with a biometric residence permit if my stay is over. 6 months.

So it seems that I can not use my old passport with the visa at the border to return and show my marriage certificate, as the customer service lady of the British passport told me.
6 MONTHS are required to obtain a new visa, or £ 839 for a fast track that I can not pay.
Anyway, I will also have my British passport, so I will not even need one!
It seems I'm completely full!
If I take the risk and try to travel anyway, I do not know what will happen.

I am legally authorized to stay here, I did not do anything wrong and I followed some advice, and now I am in a hurry!
Also, my father is old and he was in the hospital with an 80% occlusion in his arteries, and nothing good, so if I can not leave the country for the next 6 months because of this, I'm in trouble if it goes downhill down

I do not know what I can do?
Does anyone know what the deal is?
We will lose thousands of pounds on our reserved vacations if I cancel.