Sarah, Rick Alan is right to lead off in asking how you will keep your knives sharp.
So, that immediately leads into -
How are you currently keeping your current knives sharp? I'm seeing you referring to sending knives out, so my guess is that you don't sharpen your own knives. Of course, I could be wrong.....
But, if I'm not, then getting a good gyuto and some very good stones (such as "splash and go" stones like Choseras or Shapton Glass stones) will be a revelation as to what sharpness really is.
With that mentioned right away in the post, let's see if we can narrow things down just a bit.
Let's also talk about budget. You mention one potential set: the Shun Premier.
Unfortunately for my crystal ball (aka searching the Internet), the Shun Premier comes in all sorts of combinations. So, I cant't quite figure out what a realistic budget would be.
I'm also in a bind on what sort of cutting board set-up you want to consider (if at all). Home? Work? Both?
Let's tale a look at your current knives: first the Rhineland 10" chef's knife and then the Shun Elite santoku
In looking at your current Rhineland 10" chef's knife (I'm assuming we are talking about Rhineland Cutlery; see: https://rhinelandcutlery.com/10-chef-knife/), I see where it's made of "X50CrMoV15" steel (aka Krupp 4116 steel). That's precisely the same steel as used by Wusthof in their Ikon and Classic lines, and as used by Victorinox, and as used by Mercer, and as used by Messermeister, and as used by (well, plenty of mass market European cutlery manufacturers).
4116 steel is very much favored as being tough and very unlikely to chip or break. The reverse of that compliment is that 4116 steel is very difficult to sharpen. It is a very tenacious steel, and abrasion sharpening takes quite a while. It's also a steel which will not stay all that sharp for that long.
The blade profile of the Rhineland chef's knife is also with a very pronounced belly. That's going to make use of the tip somewhat problematic. You end up having to raise the handle of the knife to a high level if you want to bring the tip of the knife against your cutting board. It's a major reason I prefer knives with much shallower belly.
The Shun Elite Santoku is an entirely different critter. A simple san-mai clad blade with a Takefu SG-2 core, it's almost the reverse of the Rhineland. The core steel (SG-2) has the potential for being very hard and holding an edge, while the general santoku blade profile is much flatter than a german-style blade profile. That makes working with the tip against a cutting board surface easier with less need to raise the handle up high.
On the negative side, SG-2 steel really requires that a sharpener needs to keep the combined primary edge bevels to not less than 15o per side, or 30o combined, or significantly risk carbide loss and chipping. I'm also wondering about the quality of the SG-2 steel heat treatment in Shun knives (there have been reports of problems with Shun and other Kai knives and heat treatment problems).
Also on the negative side, santoku's in general are usually too short (180 mm) to be used as a primary knife (gyutos that are 210 mm and larger are the usual preferred length).
Mike9 is right to say that many of us will try to argue you out of getting a set. You can much better use your money for a really good chef's knife, a reasonably good paring knife/petty, a not-very-expensive serrated edge bread knife (excellent also for such tough skin/soft interior foods such as tomatoes), a knife roll and some sharpening stones - especially "Splash and go" stones. Any money left over would be better spent on your two little ones.
Hope to hear back from you about your sharpening procedures and your budget.