OP, so you say that you don't want to make your children do anything they don't want. Presumably they never have baths then? Or brush their teeth? Or go to bed when it's time? Or go to school after the holidays? Or tidy their bedrooms? The list goes on. But the point is clear, if you don't want to make them things they don't want to do, then that has to apply in every aspect of their lives. So if they were to e.g. Go to Granny's for the weekend and decide they don't want to come home, then presumably you would just shrug and accept this fact and allow them to live there until such times as they may want to come home? Presumably when your fourteen year old starts going out for parties with his mates you won't expect him to come home or let you know where he is, with whom and what he's doing? No didn't think so.
As for you stating that the seven year old is still very angry over the divorce.... that is utter bullshit. If the seven year old is angry over something which happened when he was five, then that is because you have been feeding him your anger for the past two years. Children are far more resilient and accepting than adults are. You may not want to hear it but reality is that children generally don't care about the reasons for the divorce at such a young age unless there is serious abuse or violence in the equation which it appears was not the case here.
Now, it is absolutely possible that a child may not like an incoming partner, and the reality here is that they have every right not to. But at seven and nine they are not old enough to understand the implications of refusing to have relationships with their father and their siblings. They're certainly not old enough to make life changing decisions based on the dislike of someone because their mother doesn't like her. And even at fourteen, while the child is old enough to be able to make their own decisions, they still should be given an awareness of the potential implications of those decisions, because fourteen year olds are volatile impulsive creatures who make decisions in the heat of the moment without considering the consequences until it's too late.
I have a fourteen year old who tbh hasn't taken to his dad's partner, and as such hasn't stayed at his dad's for the weekend for just over a year now. He does go there for some evenings during the week though.
We have had endless conversations over the why's and wherefores. He is old enough to make his own decisions on that score, however I certainly couldn't argue that I was doing what's in his best interests if I just sat back and let him do whatever he wanted. It would be the easiest thing in the world for me to just smile and accept that he was here permanently now and to forget that he has a father who is half of him in the same way I am. But who would that benefit in the long-term? Certainly not him. And when he gets older and realises that his half sibling has grown up and he hasn't noticed and they have no relationship, he certainly won't be able to look back and say that nobody warned him that that might happen.
He has stalled about going to his dad's for the past four years or so now. But it's only been in the last year where he has been allowed to decide for himself that he doesn't want to stay at his dad's for the weekend. And if he's committed to going there for any reason then he's bloody well expected to stick to it. And if he doesn't want to go then he's expected to communicate that himself.
My ex is my ex, not his. Iyswim.
And there is one other factor which needs to be considered. Their father is their next of kin. If anything happened to you then they would go to live with him permanently. If you have actively destroyed the relationship between them they would find this much harder, adding to the loss of their mother. I was taken seriously ill towards the end of last year, and my DS suddenly had to start spending every week night at his dad's while I was in hospital and for a few weeks after I came home and was recovering. I know he found it hard, not because he didn't want to go, but because he was dealing with my illness (we're talking about having spent time on life support seriousness of illness) as well as staying at his dad's which wasn't the norm for him. If I had died (and it was a real possibility) it would have been so much harder for him if I'd spent the past four years destroying his relationship with his father and he suddenly had to go and live there on a permanent basis.
Things still aren't perfect between him and his dad, and the reasons are his own which he is entitled to. But at least he has never been encouraged to distance himself, and my ex knows that.
We bring children up to think independently for themselves. Not so that they will mirror our thoughts and become automatons who will do as asked when asked. Remember that if you encourage that attitude then if the tide turns you will be powerless to do anything about it since it's something you have actively made happen.