Welcome to the forum!
Let me understand better why the instructions want you to split the image? It certainly is not too large for Inkscape. And it looks like it's less than 200 mm in both dimensions. What kind of machine is that too large for?
Also, how did you cut it in the first place? Generally, I think you just want to cut it in half, and don't move the 2 parts. That way, they stay aligned properly, and you don't have the nightmare of re-aligning them. But if you cut it for example using scissors, and then you scanned in the 2 parts, that could be nearly impossible to align them.
But again, I'm wondering whether it really does need to be cut in pieces.
Depending on how you cut it, it might be possible to snap the 2 pieces together, which except for using the actual coordinates and piece dimensions, would be as precise as possible alignment. Even though it might not look aligned (because of anti-aliasing) it would be aligned.
Can you share the SVG file with the 2 parts imported? Then we could give specific instructions.
Does your machine engrave from a raster image? Or will you be using Inkscape to create the vector paths for cutting/engraving? If so, it would probably work better to cut the image after it's converted to vector paths. Because Trace Bitmap (if that's what you're planning to use) will actually draw that line where you cut it, and your engraver would engrave that line. Definitely not what you want!
I'd be curious to see the tutorial or instructions you're using. That's something this community lacks, is a large selection of tutorials for using Inkscape as part of engraving or gcode cutting and etc. I've tried to write some, but since I don't actually have any cutting machine, they aren't very good. So if it's a good tutorial, I'd like to add it to our collections.