Although most people with children will treat such children equally in a Will – bar perhaps the odd specific belonging e.g. jewellery going to the only daughter rather than being shared out between all the children – this is not always the case.
There are several reasons why children may not inherit equally. There may be a dispute between the parent and one or more children. One child may be financially better-off than their siblings, and as such the parent may want to leave them less of their estate, or give this child's share straight to their own children (i.e. the parent's grandchildren). Or one child may have special needs, and thus would require more money going forward. While a parent has the right to treat their children unequally in their Will, specific reasons given in handwriting and kept with the Will can help ensure their wishes are followed after their death.
Where an adult child lives with a parent or is financially-dependent on them, I would always encourage the parent to make special consideration for this child in their Will, including giving the child the right to stay in the house, even if the estate is to be divided equally between all of the children i.e. this child would not own the house outright. Certainly, such a child could have a strong legal argument for special consideration after death if such measures are not included in the will. The child's continued residence doesn't have to be permanent; if they have a good wage, then perhaps they could be given the right to stay in the house for a year, and give them time to move?
I would also encourage clients treating children unequally in their Wills to discuss this with their children, or at least those they get on with, so there is no surprise on their death, and hopefully no bitterness because the reasons were already known.
Although I would always advise you use a qualified professional to write your Will, where your wishes are anything 'out of the ordinary', it is even more important to ensure your wishes are clear, practical and have the best chance of being implemented after your death.