That's pretty impressive that you use tap jump for wavedashing, but definitely kill that habit. You'll want to practice wavedashing using X or Y instead of tap jump. Dashdancing/wavedashing should come pretty naturally once you get the hang of that.
^^This. Like you, I had been using tap-jump on the control stick for 9+ years during my casual days. But as time goes on, you'll come to a point where you find that it'll hinder your progression, due to limiting your options (technically you'd be capable of the same things, but lots of things like short hopping, wavedashing short hopping with full/partial horizontal momentum, etc. will be so difficult to pull of consistently and throughout every match that the time/effort to master these harder versions just isn't worth it; it's an unnecessary setback). It might take just a short few days to get used to using X or Y (I would suggest Y; general consensus from our community is that it's better since it's closer to B than X is. X is otherwise just as good, and many top players [e.g. M2K, considered among the top 5 best in Melee, top...10/20? In Brawl, and prob top 5 for PM] use X primarily anyways, but it's still making stuff harder for no reason). I took 5 weeks of daily play to make the transition to comfortably+naturally begin to use X. Only real way to get it down is to just integrate it into daily tech practice, and getting as much practical experience using it during friendlies as you can (don't have to use it all the time from the start, but try to use it more and more every as the hours/days/weeks go by).
Regarding getting used to DDing and WDing at the same time, get used to using both comfortably on their own. By that I don't mean like...being able to consistently do 6 or however many in one direction or back and forth because it feels/looks cool. I mean getting used to using both efficiently+practically; their most basic purpose is to provide another movement option for spacing - baiting attacks, dodging them, and going back in to punish, or some varying order/combination of each of those. Watch vids to see how more experienced players use them on the go, and try getting used to try to using them in the same scenarios by imitating them in friendlies (preferably not on CPUs; they have inhuman reaction speeds that encourage a playstyle that relies on an unhealthy+detrimental amount of hard reads. IOW, throwing out things you think will work based on predictions of how the opponent plays...and CPUs def don't play like people do, given that their reaction speed and likelihood to always do one or two predictable actions in any given situation). Here's a
good vid advising on the mindset you should have while using these movement options to properly space yourself in relation to your opponents.
Little tidbit to answer your question more directly: DDing, as you prob know, are when you interrupt your initial dash back and forth, at varying timings. Because there are certain periods in which you can't do another dash in the same or opposite direction, without risking getting stuck in the laggy turnaround animation, you can instead WD in whichever direction you wanted to go, and then just WD again or return to DDing straight after. Put simply, using WDs between DDs can help to keep the 'flow/rhythm' of your movement going and maintain good spacing, without having to worry about getting stuck in turnaround if you need to retreat or approach towards/after the end of your initial dash. So...when using the two together, I guess I'd suggest thinking of DDing primarily, and then considering WDing in-between when/if necessary, or if you screw up the timing (you can just interrupt the laggy turnaround animation asap with a WD. That is to say, you shouldn't just cover up your mistakes and not focus/practice on reducing how often you mess to DD timings, but the option is there if it happens).