As there is real property (the house) a grant of probate IS required. This means that the will will have to be lodged in the probate office. Thus, if there is any problem with the will (it being a DIY one) this will be established.
We do not know what the will (if valid) actually says. The grandmother may indeed have left the house to one of her grandchildren and nothing to anyone else. Had your partner been alive, he could claim that she had failed in her moral duty to provide for him (a section 117 action). This action is open to her surviving children. However, this option is not open to a grandchild (ie-your children)
If perchance the house was left in the will to your childrens' father (and I'm making a HUGE assumption here) the house would go into his estate. As he died intestate, it would then pass on intestacy and be divided amongst your children. This is of course ONLY IF the grandmother left the house to your partner.
To sum up - the will will have to be lodged in the probate office. If the will IS valid, the executor is under a duty to distribute the estate according to its terms. Thus, if you/your children are entitled to anything, you will get it.
If its not valid, the estate will be divided up on intestacy - each child would get a share and your children would take the share that your partner would have been entitled to.
Hope this clarifies matters somewhat.
Caveat - I am not (yet!) a solicitor