Lee you should check out Families need fathers. You can get advice and help there on issues like this and how to progress and whether to use a solicitor or how to do it yourself if tat's how you need to go. Don't expect it to be easy or for court to wave a magic wand. It will be many month, more likely years going back and forth to court to get an agreement.
Your ds will get a free place at a nursery soon. I'm sure your ex will be aware and looking into this. Perhaps ask her what she is intending in this regard as you have a right to be involved in choices about his education and to have a relationship with nursery too.
If your ex is refusing mediation you need to have that in writing. If you go to court the judge will expect mediation to happen and if she refuses she will not be entitled to legal aid. Mediation is likely to fail because she will only agree to it to keep her legal aid most likely from what you've said.
So you go to court, go to mediation, go back to court. Cafcass likely to then be appointed to make a report, cafcass ask for more time, go back to courtm reach an interum agreement, see how this goes, back to court if it doesn't or if all good to see about progressing.. blah blah.
And so weeks turn to months. Judge will try and get you to agree, she will give a little (maybe) and you'll have to accept it. Back and forth to court etc etc. Be very sure you want to get on this band wagon nd the legal costs involved. Don't expect court to be an instant fix but long term it may be the only way to get reasonable contact sorted.
Re the issue with her not working., I'm afraid that every parent has the right to stay at home to take care of their child. Usually this is done in a relationship where one parent supports the other financially and the SAHP supports the working partner by doing the childcare etc. Sometimes both parents work and pay for childcare. But just because you are not separated doesn't mean that your ex suddenly has to find a job. In fact she will have to actively seek work when your ds is 5 (it's going down to 7 and then 6 so probably be 5 by the time your ds gets there). She will not be entitled to stay at home forever. Also she may feel she is trapped with no choice but to stay at home, live a poor lifestyle (I've been there, it's not fun) and she may not entirely be happy being stuck/trapped in that situation either.
Oh and one last point for now. This isn't about what is fair for you or for mum. This is about what is in your ds's best interests. That should be paramount in your mind at all times, not what you want or is fair in your eyes. But basically yes, a good level of contact with both parents, shared parenting if possible and parents who work together for their child's best interest while putting personal feelings aside... ultimately that is what is best for your child in most cases. Unfortunatley real life, actual and perceived hurt on both sides, and emotions run high and tend to get in the way.