Ways to counter philandering husband?

I know that he is a very philandering person so I try my best to follow him wherever he goes,to make sure he can't meet other women.His response is that he hates it and his attitute has been very hostile towards me.He just acts as though its my fault to follow him around.However,my housekeeper and babysitter suddenly had to quit and now I am stuck at home because we have three kids.Suddenly,I feel very insecure and worry all day long because I don't know where he would go and who he meets,etc.I have tried looking for new babysitter but she needs at least one week to start work.What can I do now?I really can't let him go meet other women,but I am stuck at home.I am really going crazy and I can't eat a single thing.What should I do if I don't want a divorce?