And if you have thoughts that make you feel bad, it's okay to seek help and talk about them.
A few of us I know and I discussed having those kinds of thoughts with our therapists. Those who were hospitalized explicitly requested to be admitted to a facility.
Kids will only be taken away from you as a last resort. It's usually only done if you are deemed a danger to them, and even then, authorities are usually very hesitant to do so. If this is an issue for you, seek help from your doctor or contact the Weisser Ring, an NGO committed to helping victims of violence.
My therapist told me that they can only share information about me with others if they think I am a threat to myself or others. Anything that happened in the past is not relevant. If I'm at risk of hurting myself or others, it would be best for me to go to a facility. Thinking about suicide doesn't make me a threat.
It is unlikely. We don't have enough beds in mental health facilities to care for people who are uncertain they won't act on their troubling thoughts.
If you need to go to the hospital, the kids won't be taken away permanently. The goal is to reunite you and the kids, so usually someone else will look after them until you are able to. This could be temporary foster parents, who would arrange for visits and contact between you and the kids.
My mother had expressed suicidal thoughts involving all of us kids, and it had caused my older sister to have suicidal thoughts too. If my mother had not agreed to the family's intervention, it could have led to government action.
Unless you are a danger to yourself or others, you won't be put in the hospital, and your children won't be taken away from you. As long as you don't intend to harm yourself, you won't be forced to stay in the hospital.