Hello, I have some experience of this area so I hope this information below can be of assistance. All of this is written from the perspective of you being in England: if this is not correct, none of this is valid, so please do clarify that!
I don't think your husband is lying to you, reading between the lines I think you're just confused about the situation.
£10k loan to pay for wedding/honeymoon
Calling this a 'mortgage' is technically true but not really helpful, it is a personal loan secured against the house but NOT to pay for the house, but to pay for wedding/honeymoon. Paying it off is therefore NOT a contribution to the house. Essentially this is similar to having a 10k debt on a credit card that needs to be be paid off, it is £10k borrowed to cover wedding. You may well be a party to this loan, if you've signed some papers and it was taken in the joint names of you and your DH. It sounds like you are both currently paying this off. These payments have nothing to do with your status regarding the house and don't pay a cent towards the house, they are just a debt on the side for your wedding. This debt will not affect your relationship to the house either morally or legally.
Current ownership of the house
As I understand it, you currently do not have any ownership of the house. The house was bought by DH in sole name before your marriage. He paid with a substantial deposit and the house still has a mortgage to be paid (not just the mortgage above, but one used to purchase it). Eg he paid £800k for the house, £400k was deposit and £400k was mortgage. Both mortgage and house are in his name.
Equity in the house
It's really hard to advise on this without understanding even roughly what the house is worth and what the equity is. This could be a situation of him having already paid for most of the house, or it could be one where (assuming you stay married for a couple of decades) you both end up paying for it. Regardless, as you noted, your moral right to the house would change substantially over time and this should be reflected in estate planning.
The house going forward
When is the current fix on the mortgage due to end? This would be what I would be thinking about in your position, if we assume it is likely in the next year or two.
Option A: new mortgage, tenants in common (50/50) for future payments with his current ownership ringfenced
When the mortgage fix is changing, I would want to take out a new mortgage in both of your names. He should ringfence all of his contributions and deposit to date, in his own name, and you should agree to pay future mortgage contributions together as co-owners for the remainder of the mortgage term. This would mean you would own ONLY the portion of the house that you contributed towards. So if £400k (half of original value) has been paid already, and you together paid off the full mortgage, you two would together both own the next half (£400k) of the house (so you would own one quarter, or £200k of the house, although of course the value of the house changes over time). The shares could be fixed either as percentages or as lump sums, he would likely prefer the former to reflect how his early contributions have grown over time (eg 20k paid 20 years ago should be worth a lot more than 20k paid 2 years ago).
What would happen if you divorced
If you divorced under option A in the next few years you would likely be awarded your potion of the equity (likely a lump sum of a couple of thousand, which he would need to pay you when buying you out) and he could remortgage in his own name. The house would go back to being 100% in his name but you would have a chunk of money reflecting your contributions. You have a short marriage and no young children together so this would be the likely outcome.
What would happen if he died
The house would be likely need to be sold. His ringfenced money would pass under his will (see below), then the remainder of the equity would be divided 50/50 between his estate (and passing via his will), and to you. So this would mean if he died in a few years and you had not made many contributions, your direct ownership share would be thousands but not significant. However if he died in 30 years it could be very substantial.
OR OPTION B
The situation is more complex if he does not want you to co-own the house in the future of your marriage. In that case, you need to consider investing your money in other assets, not contributing to things like improvements etc and instead put the money into ISAs etc in your own name. In this case I would (personally) absolutely not be paying it into life insurance. Your main problem here is not the issue of what you pass on to your children, but the issue of how YOU would be housed for the remainder of your life. Your focus should be on ensuring YOU have assets set up for you in the future, then you can have these go on to your children after death. Planning assets for your children when you have not provided for your own old age is madness.
The house in the will
This is separate to the ownership of the house. If as above your DH owns the house in his own name then legally it is entirely his own decision where the money from that goes on his death.
The 1/3rds
It sounds like he has told you that he has set things up so that if he were to die shortly you would receive both his pension and 1/3rd of the equity of his house, with the other 2/3rds going to his children. This sounds like a good set up as you would have a substantial deposit you could use to purchase a small house in your own name, plus a pension, while his children would immediately get their inheritance. You'd be able to remarry and decide where to live. You need to remember this is NOT 1/3rd of the house that you actually get, it is 1/3rd of the equity, so if the house value is £800k it is a very different amount if there is a £400k mortgage remaining or a £100k mortgage left!
What the will does not do
However I think you are slightly confused about the status of a will. This 1/3rd of the house is only relevant if he dies, and if at his death this will is still the current will. He's entitled to change it if he wants, and would certainly do so if for example you split up. So as you can see it is a separate question to the matter of the current ownership of the home.
If you died now
If you died now, you could only will to your children what you actually own. So this is your savings, your personal effects, etc. You can't will to your children 1/3rd of a house that you have no ownership over! So if leaving money to your children is important to you, I would focus on (a) staying alive for a good while! and (b) accumulating assets in your own name. You should also note that joint savings with your husband (such as a joint account) pass automatically to the surviving spouse, they do not pass under a will. So in the short term have savings accounts in your own name to have something to both protect yourself and to pass on if you die.
The often mentioned 'life interest in the house'
This would be to give you the right to stay in the house for life on the spouse's death, even if the will gave the entire thing to the children. I would absolutely not be looking at this at this point in your case. This works well when you are thinking of elderly spouses who need somewhere to live with the assumption of it only being a fairly short period, or where you essentially want to give your spouse a house but ensure the money after their death still goes to your children. In the case of a short marriage that has not produced children, he has no moral or legal obligation to provide a home for you for life.
Firstly the house is mortgaged: unless he has a life insurance paying off the mortgage on his death, there isn't a whole house asset to pass on. There's potentially a big mortgage left to pay and you'd likely have to sell it anyway.
Secondly it would be a very poor outcome for his children. You are in your 50s and could well live for even another 50 years. The children would have legal ownership of a house (with related responsibilities and costs) but no actual asset, they could be dead before they get their inheritance. This would not be a good outcome legally or morally at this point.
Thirdly it would not necessarily be the best outcome for you at this point. It wouldn't give you anything to pass on to your children, you also wouldn't have the ability to move/downsize to fit lifestyle. It would cause family resentment, especially if you had a new partner. If he died tragically tomorrow, and you remarried in 5 years, do you think it would be fair for you to still be living in a house legally owned by his children for decades to come?
So...what should you do?
You need to speak to your husband and with professionals about estate planning. You need to separate out these strands:
1: ensuring you have some support in the case of your DH dying in the foreseeable future, which should be aimed at getting you into a strong position for the remainder of your life while passing the majority of his assets to his children
2: getting the structures set up so you can grow your own assets in the future, so having savings in your own name that you can then eventually pass to your own children