Melon

Here comes the graded version. Awe-inspiring coin! The only problem is it's hard to photograph (updated with better lighting)...

 

This has turned into a very interesting conversation! This is all new to me, so very interesting to hear from you all. Obviously I'm rooting for them to be genuine, but if not then I'd rather be aware. Then I can decide whether to keep them purely for weight, sell them on (for gold content only with clear disclosure of course), or have a discussion with the dealer I purchased them from although I'm doubtful of a favourable outcome there.  
From what I'm hearing above, it sounds like the details Booky mentioned may actually be a good sign if it is indeed a 'reverse A design 1903 Sydney' coin, as would match the expectation. Sounds like I need to better identify the mint mark and get a better shot of the coin surface to reveal clues as to whether it was struck or cast. 
Tomorrow I will have hands on the two coins in question and intend to try and capture (A) better lit photos, (B) accurate weights and (C) accurate dimensions. Had some new toys arrive in the post to help! 😄 Will post the findings 👍

It depends if it's a London or branch mint. If London and 1903 it won't have a BP.
If 1903 and branch, it will have to be Sydney but still won't have a BP. Melbourne doesn't exist.
Thus, it will be a Reverse A design, there should be a larger gap around the G&D design than the later years.

I've spotted some things for you to check:
There's no BP initials by the date. The dragons claw below its ear. Looks like it's lost its fingers and the gap between the ear and claw is larger than on the other coins. The gap between the end of the horses tail and the end of the broken lance is bigger than the other coins. Overall lack of detail, even though it's worn, remind me of the modern £1 coin forgeries.

Take close ups of surface in a brighter light, that way we could tell if it’s a cast copy. 

That’s definitely a different mint not LONDON.  Looks like another M 

I'm actually drooling at these photos. Bravo. 
Here's a fun one of my own 😄

I don't have any experience of keeping half sovs in tight capsules but in general, any size difference doesn't bode well. I would imagine it would show up the slightest of diameter intolerance.
The 1903 looks very suspicious, especially the rim which looks too thick and uneven. It could be the photo but the whole surface of the coin looks grainy and pock-marked, the field at least should have that nice smooth matt appearence.
I can't see anything obvious with the 1915 but again, it does look to have uneven texture in the field. George's chest looks very flat and lacking detail even though the coin as a whole isn't very worn. However, I think I have seen this before with branch mint halves. Having a close look at the tail might reveal something if it was compared against a known good example.

Can’t make it out on mobile but looks like the 03 has a mintmark too

Don't expect a bullion dealer to necessarily be a numismatic expert, someone like HGM or Atkinsons are only going to guarantee its 22ct whereas Chards may be more on the ball.
Unless you paid a premium, don't worry.

I have only about 15 half sovereigns they are not my thing. But having said that I collect sovereigns, to me the Melbourne sovereign looks not right on the reverse general lack of detail.    I know it's worn, questions like lack of detail in the ground!   Ask Sovsteve to have a look.  
I agree the 3rd side damage would make the coins harder to fit a capsule.  Also there are some very good fakes around that time plus some badly struck correct ones.  

So happy to hear that - congratulations! 😁

Ahhh... I'm never gonna trust your coin pictures anymore for sale!  😛 

Lovely coin. I've given her a quick wipe down and a polish for ya. 

To be honest, I'd put the problem directly to the Royal Mint. If they sell to your location, they need to accept returns from your location when the item is defective. 
Ask them what shipping service they would like you to use to return to them and ensure they are comfortable covering the cost and any risk of loss in transit. In any event make sure you get proof of postage. 

My mistake - I was blinded by all those gold Brits, didn't even notice the 50 Peso in the middle! 😊

Visited my safety deposit box today and put the recently acquired Gold with the rest of the Gold stack. Don't visit Safety Deposit box that often maybe once a year and took opportunity to take some photos. Gold bullion occupying 25% space in the box the remainder family jewellery. Still enough room in the box to add another 40 oz Gold in Royal Mint tubes to finish off Queens Beasts series.
Gold bullion square red box total 74.25 oz.



 
 

I am with Karl, the Melbourne mint one is most likely the reason. Also bonus, if I recall it’s the lowest mintage GV half sov.