Many (probably most) people have life insurance tied to the mortgage, which pays out in the event of death, clearing the mortgage debt. If she has this, there's no problem, so check that out first. You may be in a better position than you think!
Looking at it from the point of view of you (that's you and your dh) being the executor of the will, what would normally happen is that you would 'realise all the assets' (sell the house) and then distribute the money(after paying off any debt) to the beneficiaries. So you'd put the house on the market, and wait for offers. Once you get one, you sell to the new person and pay off the mortgage, and dole out the money.
As your mother's pension beneficiary (which is usually separate to the assets for the will), you/dh will get that money without (probably before) the estate is settled. Now you have a lump sum for a deposit. You could go to a mortgage broker or provider and ask for a mortgage 'in principle' while you look for a house to buy.
Oh look! by coincidence, the one you're currently renting is on the market - and you'll only need a tiny mortgage to buy it, what with the huge deposit you've got! How fortuitous - why not put an offer in with the estate agent?
So check out - is there mortgage insurance? Is the pension payment part of the estate, or is your dh a 'named beneficiary' of the pension (and therefore its not part of the estate)? You'll probably need to get a couple of different layers involved - one to ensure the rights of the will's beneficiaries are served, and one to ensure the rights of the house buyers are served!
Legal advice and independent financial advisor advice probably very worth taking to check if this is how it'll work (I am not a lawyer)