YANBU
She's completely unreasonable and obviously got a lot of control issues.
Don't worry about the current lack of PR. Your fiance has an ongoing relationship with your stepson as his father and as his father is allowed to apply to the court for contact regardless of whether he currently has PR. He can apply for PR at the same time at no extra cost (though it is now a separate application form). He is almost entirely certain to get PR - it is only very very rarely that this would be refused.
I would start the legal process now. There are no welfare issues, contact has previously been established and once a month is very little time for your stepson to see his Dad so your chances of success should be high. I would think you could well end up with much better contact tgan you now in fact. But you aren't going to get anywhere without getting serious I fear. However, if you are lucky, you'll be able to resolve it without having to go through the whole court process to a final contested hearing.
Your fiancé will have to make the attempt to engage her in mediation before you are allowed to make the application. To give you an idea of the process and timescale, what we did was this:
Your partner writes formally to ex stating what contact he wants eg one weekend a month from Friday evening to Monday morning overnight with 50% holiday time at your home. Think about what you would ideally want for your stepson eg alternate Christmase are quite usual and can be included. He also suggests they attend mediation.
In our case this was declined by ex that week and so solicitor wrote repeating the same with request to reply within 2 weeks. Ex replied saying she was still not willing to attend mediation.
My DP attended mediation assessment session on his own and the mediator then contacted ex. She refused to attend. The mediation session was within the same week he requested the appointment and it took about a month for mediator to contact ex and for her to refuse.
At this point solicitor put in application for contact and PR. It took her about a week and we heard back from court the week after with first directions hearing for 6 weeks time. At this point ex got herself a solicitor who persuaded her told her she had no choice to mediate.
She attended a mediation meeting 2 weeks after receiving court papers and they both went to mediation. Not much was agreed in the first session but they met in 2 weeks time and agreed the contact pattern DP wanted. :)
We requested the court case was adjourned for 4 months to test out the agreement and a further mediation session was agreed in 3 months time to try to ensure things were kept on track (she had continued to be difficult about a couple of issues). The further mediation session went well, the court date was adjourned once more and eventually cancelled.
The whole thing took about 8 months but contact had improved drastically within even a few months. She got advice from her solicitor that she didn't have much of a leg to stand on I think :)
If you are unlucky enough that forcing mediation doesn't work then you will normally have a mediation session/discussion with a cafcass officer at the first directions hearing. With my ex partner (who also had contact issues with his children from his first marriage - I am destined to be a stepmum!) this is where things were largely resolved and a contact order was made then and there with a further review date being booked by the court. They never went to this as managed to fine tune the court order via mediation before that point. If you are unlucky enough to have to go to a final contested hearing then I believe it takes about 12 weeks from the directions hearing as CAFCASS are likely to have to make a report.
Most cases are resolved prior to this though. It doesn't sound like there are any welfare issues which can take longer to resolve fully. The courts do like the status quo so you should easily get back what you used to have. If you want an increase in time this should be possible too, given you only see him once a month but that may take a little more time with gradual increases in contact.
If it isn't resolved in good time for your wedding then you can ask for that as a separate order I think. There is no need for her to be there!
The trick with it is to see it as a slow gradual process and don't give up. Really try to give mediation a go too. Your partner doesn't have to agree to anything he feels uncomfortable with (and mustn't do this!) but it really is amazing how much progress you can make with the most unreasonable of people this way. I think everyone going into mediation says their ex is far too stubborn/unreasonable/crazy for it to work and we thought this too. Sometimes that is the case but it's much more common for it to work.
A good solicitor is invaluable although I understand it is pretty easy to do as a litigant in person too.
Good luck and congratulations on your engagement!