If you only think he is drinking, it is worth checking and making sure that he and your step-mum understand how important it is. If he is dehydrated, his constipation is only going to get worse.
When you speak to the hospice tomorrow, it might be helpful for you to ask whether they believe he is moving into the end stage. It is really important that you try to have that conversation with your dad as well; it will be easier for you to support him if you understand his wishes. For example, he may already have agreed that he would not want to be put through any life-prolonging treatment and / or, being under the palliative care team, it may be marked on his medical notes in which case phoning 111 might be not the right thing to do. Usually, when someone is in palliative care, problems are dealt with by the hospice / Macmillan nurses and GP.