"I have been told by one solicitor that having trustees is not necessary."
There is a body called the Society of Trust and Estate Practitioners (STEP). They have solicitors who are very experienced and knowledgeable in this area. If you search something like "STEP solicitor [name of your town]" then you should get a list of solicitors who have been accepted as full STEP members.
I would really recommend that you speak with a suitably qualified solicitor.
Yes, you certainly can leave your house directly to your children. You can leave your house directly to them and, since your children are over 18, they will own the house once probate has been completed and the executors have filled in the paperwork with HM Land Registry.
Once that is done, your children can immediately apply for a court order to sell the house and turn your DP out of the house. Tough luck on him, he doesn't get any say in the matter.
In contrast, if you leave your house in trust to your children when you die (it is often referred to as an 'immediate post death interest trust') then you can stipulate these conditions, eg that your DP is allowed to remain in the property for X number of years.
You mention that you want your DP to have a certain share of the property. Again, a solicitor will advise you on this. So you leave eg 90% in trust to your children and 10% to your DP. That way, when the house is sold your DP gets his 10%.
If you absolutely want to ensure that your DP stays in the house for the defined period, eg two years, then you need to leave the house in trust to your children and give your DP the right to live there. Otherwise your children could turn him out of the house quite quickly indeed.
It is quite common for the executors to also be the trustees.