You'll probably find that the judge will bend over backwards to help you if you're self repping.
If your ex hasn't lodged his application yet, suggest mediation first. He may refuse, but at least you can draw the court's attention to the fact that you tried to settle out of court. If you do go to mediation, there is a chance that you will settle it.
At the first hearing, the court won't want to hear any evidence from either of you. Usually cafcass are there in the court building so the judge will ask you and your ex to meet with cafcass there and then to try to reach agreement. On the assumption that you can't agree, then you go back in to see the judge and he or she will make directions orders inc. provision for each of you to file statements setting out your side of the story, and usually for cafcass to then file a report setting out their recommendations as to whether shared residence (which does NOT mean 50/50 share of time between the parents), an increase in contact, or keeping the status quo.
Do not refer, other than in passing, to the DV issues. The court is unlikely to consider them relevant several years later, after contact has been going ok for all that time.
The courts these days are a bit more keen on shared residence where the parties live reasonably close (say within about 20 miles), and they can communicate, which I presume you have been managing for the last few years. The best argument against shared residence in my experience is that children like to know where they live, it's that simple. In the words of an experienced barrister who I regularly instruct, they like to know where they keep their football kit. I have had many disputed shared resident cases and I'd say there's a fairly even split between judges approving shared residence and finding against it.
Once you have the cafcass report, unless there are proveable factual inaccuracies, the best thing to do is frankly to accept it even if you don't agree with the recommendation. This is because Cafcass are the eyes and ears of the court, they are trying to find what is in the child's best interests and often that is not what one of the parents thinks is their best interests.
If you aren't happy with the cafcass report then the matter will have to go to a final hearing and you will have to cross examine the cafcass officer. Only do this if you are absolutely certain that the recommendation is based on factual errors of the cafcass officer, not just that you don't like what she is recommending.
I know I'm painting a bit of a negative picture here, the reason for that is the number of cases I've seen (had one yesterday) where the cafcass officer recommends increased, unsupervised contact, or shared residence but the report is not accepted by the mother purely because of the history with the dad, and often linked in with that is the fact that children notoriously try to keep both parents happy by telling them what they think that parent wants to hear.
If your ds has so far enjoyed contact visits, and his dad wants to play a more active role in his life, and if the dad looks after your ds well on contact visits, there are no concerns about neglect, abuse, etc then the chances are that contact may be increased. This may be called a shared residence order but may only mean a difference of a few nights extra per month in effect.
Sorry this is long and a bit negative, but best to be prepared for the worst but at the same time try for the best.
Good luck.