As is often the case when life interest trusts are discussed on Mumsnet, there is a lot of misinformation on this thread. Unless this is not a normal life interest trust, some of OP's posts suggest she has misunderstood how this works. If she is uncertain, she needs to consult a solicitor.
If this is a normal life interest trust, OP's partner's share of the property will go into trust when he dies. It will NOT go to the children at this point. They will NOT own it - it will be owned by the trust. The fact they will ultimately inherit his share of the property does not give them any rights. The only people with rights and responsibilities are the trustees. This may be the children or it may be someone else. People often appoint their executors as the trustees. If the children are not the trustees, they will have no right to interfere.
OP will be responsible for day-to-day maintenance and upkeep of the property, keeping it in good repair, just as she would be if she owned the whole house. The trustees are responsible for ensuring that the property maintains its value but, beyond that, they cannot interfere.
If major works are needed such as a new roof, what happens depends on what the will says. It may be OP's responsibility (as it would be if she owned the house) or it may be up to the trustees to pay.
The trustees cannot demand changes to the house. For example, they can insist that the kitchen is kept in good repair, but they cannot insist on a new kitchen, nor can they insist on building an extension.
If OP wants a new kitchen or bathroom, or to extend the house, she will need the approval of the trustees who will need to ensure that the planned change will not damage the value of the property. That does not allow them detailed control over the change. If, for example, OP wants white kitchen units, the trustees cannot insist on green, nor can they refuse to approve the change just because they don't like white.
If OP wants to downsize or move elsewhere, she will be able to use all the proceeds from the sale of the house to do so. The trust will own a proportion of any new property she buys. Any surplus funds that belonged to the trust would be invested and OP would receive any income they generated.
If OP needs to go into a care, she will be able to use the equity in her portion of the property to pay for care. The equity in that belongs to the trust will not be taken into account in determining whether LA funding is available.
The above assumes this is a normal life interest trust. As I say, if she is in any doubt OP should get proper legal advice.
This arrangement generally works well. Unfortunately, sometimes it does not and the children harass the surviving partner. Sometimes the surviving partner does nothing about this, either thinking there is nothing they can do or being unwilling to take action. However, if the children make unannounced visits to the property, make threats or engage in alarming behaviour, the surviving partner can get an injunction to stop them. If the children are also trustees, even if their behaviour does not cross the line into harassment, the surviving partner can apply to have them removed as trustees if they are hostile or acting unreasonably.