OP, I think you are going through a hard time at the moment, so first of all you need to give yourself a break about how you are feeling about this. You are feeling upset and I think that despite what other people or I say or think, how you are feeling is how you are feeling.
I find its really hard sometimes to look at myself and evaluate why I'm upset with a situation and why others are considering things from a more logical and calm viewpoint. But sometimes I still need to hear those views so I can bluster and rant, but then think through their points to see things in a new light.
So be abit gentle with yourself, then step away and look at this situation as though you are a stranger hearing about this from someone else. Think about what people are saying and where when you really think about it, you would if it were someone else they were discussing, would be agreeing with them.
I don't know your situation only what you have said, I can only understand things you've said and from my own personal experiences.
I don't have step children to deal with, I hope that if I did I would want to think of them and value them as much as my own children.
My two children are now in their late teens, but I do remember how hard it was when they were little as there was only 18 months between them. One of them is also on the autistic spectrum (which we didn't find out till Yr 1 in Primary) and had very difficult behavioural problems. Life was challenging and exhausting. I also had no support from family. My mother was too elderly, the rest of my family were 2 1/2 hours away and my husband's parents and family who lived 20 minutes away were not interested in helping at all. My friends were also snowed under with their own young families, and because of my youngest autism often found him difficult to cope with.
My husband works in IT in a fairly rare specialist role. The two companies he worked for over the time our children were babies and through primary school constantly sent him away. Constantly.
Overnight stays, 2-3 days, a week, 2 weeks, a month - in the UK, Ireland, Europe, US, China. I remember him being sent away a few weeks after our second child was born, and what made him resign from the first company was when they sent him off to the US for 2 weeks whilst I was still in plaster.
I also remember being rushed into hospital with meningitis when my youngest was a baby and my eldest was a toddler both of whom had the winter vomiting bug and had been ill for 5 days running whilst we had building work going on. My husband was on a work trip in California and couldn't get back because the airports were closed because of wildfires. My in laws didn't want to catch anything so sent someone else to look after my children and didn't come once to see me in hospital. The person looking after my children came twice so I could see the children once I was able to have visitors but I literally only had a hospital gown for a week before my husband managed to finally get home.
It did vary how frequently he was sent away but one particularly memorable year we worked out he'd spent 5 months away from home with trips to the US. That involved him being home for a couple of days or a week, then going off out to the US for anything from a week to a month.
I remember being very frazzled. Very emotional and very, very, very exhausted. Its not easy when you haven't got that extra pair of hands, that other person to say help me with such and such so I can have time to eat or take a bath. It is exhausting, and being on your own with young children without support is challenging.
Now I know that my situation back then wasn't the same as yours. My husband went away for work not for pleasure, but I'm glad to say that no matter how hard it was for me I was always understanding it was something he had to do. It was part and parcel of the job and the person he is. I never begrudged it, I missed him, was relieved when he got safely back (I always remembering watching the Twin Towers falling while playing on a rug with my oldest as a baby), but I never put a big guilt trip on him or openly resented it to make him feel bad. It was just something that happened as part of our family life. And in fact to this day when he goes off somewhere he's having to fly to, I put a secret card and a letter to him hidden in his case to let him know he's loved, missed and I'm looking forward to his return.
It was my job as a mum and a wife to keep things going and support my children and my husband. That is part of being in a family which loves and supports each other.
Now he doesn't travel as often and my children are now young men. And over the years I've gotten back into doing work and things for me.
But I do remember those years and so I am sympathetic to your problem of no support for those 5 days. I also understand that he is going away to the US to take his daughter on a birthday treat while you are at home with three young children. Its a jolly not work. I also understand about the whole money side of things. We had it quite tight for a number of years while the children were little.
But, I think you need to put things into perspective and take a real hard look at yourself and why you are feeling this way. I don't want you to switch off, and I don't want to tell you I think this or that. I think you need to ask yourself some hard difficult questions, look yourself in the mirror and answer them honestly.
Is it the money (which you agreed could be spent on this trip)?
Is it that you feel you are not able to cope with your children?
Is it resentment he will be enjoying himself?
Is it jealousy that he is not treating you?
Is it jealously and resentment that he's treating his daughter - your step daughter and therefore not a child of your blood? Would you feel that way if one of your children were 21 and he wanted to treat them?
Do you begrudge her having her dad to herself and that he's making a big thing out of what is an important and significant coming of age birthday?
Do you resent that he has a daughter who isn't your child? Are you jealous of her?
Are you feeling abit insecure of your place in his affections within the wider dynamics of his family?
Are you feeling taken for granted and unsupported by your husband generally when he's at home?
Are you feeling exhausted and depressed? You may not realise you are depressed.
I had PND after my first son and he had colic plus we were waiting to hear if he had inherited a neurological condition I was diagnosed with when I was 2 months pregnant. I was NOT in a good place and it made me very emotional, irritable and not always very reasonable. Unimportant things would set me off big time.
Think about the above questions and answer them honestly. I think if you do you will understand what is generating your anger about your husband spending 5 nights away with his daughter. I hope you resolve this conflict and resentment you feel and are able to talk things through honestly with your husband.