My advice is stick to your guns. It is your bathroom and you want it perfect. We had a problem with our grout in our bathroom floor (it was discoloured and could not be improved) so the tile contractor regrouted the whole floor. It was a major job, but are happy it was done. I don't know alot about tiling, but a crack in the grout in the shower sounds alarm bells in my mind.

For a DIY repair? Manual tools include a simple grout saw, something along the lines of this: To something powered, like a diamond bit chucked in a dremel or rotary cutoff tool: In a shower you simply want water shedding down the face of the tile and grout. Behind your tile is a tile backer board of some sort. Not knowing the age or construction of your shower, this could be anything: greenboard, cement board, gypsum core board with an acrylic facing, or a floated wall of mud. With these types of construction, your tile and grout are your first line of defense in preventing water intrusion. Behind those tile backers should be a water shedding membrane of some sort; 6-mil poly or tar paper on the walls, and CPVC/CPE membrane on the floor pan and lapped up the lower 10" of the walls. That is your final layer of protection, your only true "waterproofing". When cutting out grout you only want to cut the grout, you don't want to cut so deep that you go through the backer and into your waterproofing membrane. In a shower with a topical waterproofing membrane, where you have either a sheet membrane (like Kerdi) or a trowel on membrane (like Redgard) right behind the tile, you don't want to cut full-depth into the grout joint as you don't want to damage that topical membrane. In showers with a topical membrane like Kerdi, cracks in grout are more cosmetic than anything else, for water that gets through cracks in the grout still will not penetrate the Kerdi. In showers with a membrane buried behind the cement board, or with a CPVC or CPE liner buried in the middle of the shower pan, I'm more concerned as I want no unnecessary water getting into and wetting the tile backer board or cementicious substrates in the walls/floors. In that case I'm more protective of the grout on the walls or the caulked inside corners, I want to keep that first line of defense in top-notch condition. The difficult thing is not knowing how the shower was constructed, and even more importantly, how well the detailing was done. That's why, even though tile and grout are not "waterproof" per se, you still want to protect the integrity of that first line of defense as best you can. Mongo

Looks like of change of plane, going from a horizontal to a vertical surface, for example. The grout is crackig on an outside corner? The cracking is most likely caused by differential movement. As to the structure of the joint, I'm not certain of what's under the tile. If there is wood that is getting wet and swelling, that could be causing the movement. If green (not kiln dried) lumber was used under the curb, that could be causing the movement. If you used unsanded grout on a too-large joint, grout shrinkage could be causing the cracking. I'd prefer that your joint have the horizontal tile on top overlapping the vertical tiles on the sides so the grout joint is on the "side" instead of on "top". Remove the grout and caulk the joint instead. Caulk can flex and handle movement better than rigid grout.

Really recommend you get an onsite inspection, analysis and discussion with a very qualified tile contractor (not the folks who performed the work). There are several approaches to this. None are effortless, but onsite is a must, and a pro is a must. You already know you have issues. No more advice from the internet will solve them. If you are near any of these certified contractors, that is one place to start. https://www.ceramictilefoundation.org/find-certified-tile-installers Or referrals from trusted sources locally. Where did you buy the tile? If it is a quality tile supplier, they may be able to provide you with the "A list". And yes, re-visit the "curbless" in your situation. At the very least, a small threshold, but this can be discussed along with the other issues with the Pro.