I don't understand why all day while she is at work or out there aren't any issues. We go on walks, to parks, play with toys, the day is focused on him. I understand that she is the favorite parent, she is more lively and shows emotion better than I can. How can I help the situation. His mother gives me all kinds of advice and I try. Sometimes I do feel rejected and I get angry because the mood changes and I feel like the enemy. Usually they have a routine in the mornings and I try to follow that. If I change one thing or try anything different he will be really upset and it will almost stay that way the whole day. It puts up a wall that I can't push through. I can't find much online to help a father with a highly functional autistic child with issues like this.
What this answer will not focus on: I guess you already know that many autistic people have a hard time with changes to fixed routines. I assume there are tips about this that can be found online - otherwise this facet of your question might deserve to be asked in it's own question.
What you describe: You write that he is okay when he is only with you or only with his mother. When he is with both, he reacts badly towards the (pardon me saying so) 'secondary' care-taker.
What is the matter:
- Being among many people is taxing for people on the autism spectrum.
- It is also hard to understand what people feel/want/demand, since part of this is always non-verbal aspects that are hard to read.
- A third hard thing for people on the autism-spectrum is handling conflicting information or conflicting demands.
While he is only with you or only with his mother, there is only one "important" person he needs to focus on. Other people (kids, other adults) may be around, but can safely be ignored whenever things become overwhelming.
But when he is with both of you, there are two faces/gestures/voice-inflections that he needs to interpret constantly. Which is way more taxing.
To make the situation worse: There will inevitably be conflicting demands on him. His mother may have set a rule ("First brushing the teeth, then putting on jacket, then putting on shoes"), but you might demand a different thing ("Do put the shoes on now, we can get the jacket later!").
This may feel horrible to him. It feels like two drill-sargeants shouting contradicting orders at you. Or like having to break one law in order to follow the other.
Since his mother is the "normal" person for these situations and you are the "interfering one", he will lash out towards you, not her.
So, what can you do?
Make clear who is in charge. When his mother is handling things, show clearly that you are not going to make requests. Do relax (and look relaxed!) in a chair if necessary! If/when you have to be in charge, do a clear "handover" of authority while the child is present. Could be something like: "Dear [mother], can we try a daddy-day today, where i and [child] decided the rules?" Obviously, it should be the mother who should not interfere anymore after such a handover.
Switch to suggestions and questions: "The shoes are still dirty. If you want to, you or I can clean them before you put them on." Make sure these are real suggestions/questions, not just demands in the disguise of a rhetorical question. Accept "no" as an answer. Do be aware that even questions can be taxing in a stressful situation.
Your emotions and stress do increase his stress level. So enter these situations as relaxed as you can, and avoid anything that makes you feel stressed or emotional.
For your child, emotions can be a vicious circle: He might suffer from your emotion and the stress you add to the situation. But if he complains about you, your emotion will become even bigger. This, by the way, might be where the feeling of hatred comes from. There simply no simple way out for him. From his perspective, you are the original source of stress, and you escalate things whenever he tries to tell you that he needs you to stay away.
That all being said: Thank you for what you are doing. Good luck in making things better and better.