Deeeedee, so sorry to hear about your loss. Dealing with the practicalities of a death can be so very difficult for everyone involved. I had to do it recently with my sibling and it's so horrid, so please don't think I don't understand with the following!
From a practical perspective if you want to keep the house then your options really are for you, your non executor sibling, or a combination of both, to buy out the sibling who doesn't want to keep the house. I would definitely echo all of the advise above about speaking to a financial adviser as without knowing your specific financial situations it's very hard to say what options you have available. But, a few things to consider:
-What else is there in the estate e.g. cash or investments? The will says (I think) 1/3 of the estate but unless it's very specific that will mean 1/3 of the value, those 1/3rds could be made up of different assets. So if there are assets other than the house you and sibling 1 could agree to all of them going to sibling 2. This could reduce how much you need to find to buy sibling 2 out
-have you had the house valued? At this stage for the purposes of planning you could get a couple of local estate agents out to give you rough prices but if you go down a route involving a mortgage on your dad's house then you will need to get a full home report done. Check locally for quotes, think ours was about £600 last year.
-Depending on the value, you, sibling 1 or both of you might be able to take out a mortgage against your dad's house. You will need to speak to an adviser about this and think very carefully about how you plan to use it if you manage to keep it as that will influence which mortgage products you can be offered. I'd maybe look for someone who specialises in non-residential (i.e. BTL and holiday lets) as they will know the market better.
-Alternatively, if either or both of you own your own homes is remortgaging to release some equity an option? Would depend on your incomes, property values etc but could be an option.
-without knowing the property, is there any part of it which could be split? MIL had to do this when her dad died as there was a large garden and a separate garage and selling them meant the main house could be kept. Obviously very location and property specific but worth mentioning.
-Stamp duty will be payable on the value of the transaction rather than the property, although I think if I remember correctly the land registration fees are on the full value.
Practically, if you would like to keep it and use for a holiday let then have a think about how you would manage this and what the costs would be. We have friends who own a holiday home in the highlands and they have a local lady who comes in and cleans between tenants, holds keys etc but obviously she gets paid for this. You'll also need to think about what holiday letters look for and whether you'd need to make any changes (maybe in terms of furnishings, obviously you would want to remove personal items to protect them too) and also whether there are any regs you would need to comply with.
Whether it's rented or not you'll want to insure it although as mentioned upthread this can be tricky on an empty property. DH's dad lives abroad for part of the year and DH has to go round and check on the flat regularly (weekly I think but may be less) as one of the terms of the insurance!
You'll also need to think about the tax - you'll need to declare any income from renting it out (self assessment will be needed if you don't already do one) and you'll have to pay capital gains if you eventually sell in 10 years or so as you suggested.
Be kind to yourself, it sounds like you have been through an awful lot in the last 6 months. It's understandable not to be ready to deal with all of this. Use the couple of months to break it down in to bite size chunks and take it slowly.