Familiarity can bring safe feelings. Whether that means he brings certain items and objects from home that provide comfort or if you can manage to spend time with him in the shared space together to assure your child that it is safe, these are all ways to relieve his anxiety. Also being around the people he is staying with can help as well. Also provide him with activities and plans for while you are away so that he can have other activities to focus on.
It is natural for children to feel these emotions to some degree when left without their parents. Always reassure you will be back and let them know that you care about them deeply. Also let them know that you being away provides them with an opportunity to make some new friends! If you can frame it as an opportunity, it may help adjust their interpretation of the event as well. If their behavior is worrisome or truly out of control, than it may be worth consulting a child psychologist about what is occuring.
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Is he staying with a familiar sitter? I would start by talking to the sitter about different activities to try out or maybe would take his mind of of yall not being there. Having a sitter that actually takes the time to spend quality time makes a difference. Always be honest with him and tell him you are going on date night with dad, and that you will return at a specific time, and for him to have fun, and you will see him after your date night is over. Let him know that when he is on good behavior that both you and your husband will give a special day for the three of you to do something special together as a family. Get a jar and fill it with his favorite things to do, so when he is on good behavior for your date night, or whatever you want to call it, then he get to take a pull out of the jar. Try that. Just reassure him when you are dropping him off that you will be back for him, and don't stay long enough for him to pout and put up a fight. Having a good caregiver while you are away makes a world of difference. Make sure that you sit down and visit with this caregiver whether it be a relative, or friend. Sit down for coffee or tea and discuss a plan that might make him feel more comfortable. Maybe you just need to find someone else to watch your son. Sit down and ask your son what he likes about the sitter, and what he doesn't like about being there too. Hope this was helpful.