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You should talk to him about it before you decide to marry him, don't marry him without resolving this issue or else the children will learn to resent you for not protecting them and they will feel like you chose him over them and that will only make them act out even more. Your boyfriend has to realize that he is being too harsh and that he can handle it another way. Your children may be acting out because all children want their parents together and don't want to see their mother with anyone but their father, depending on how long you have been together they may need some time to get used to the fact that you and their father won't get back together. If he is a good person other than being harsh with your children then I would suggest talking to him and asking him if he could be a little more patient with the children and explain to him how difficult it is for children when their parents divorce. Your children need you right now and although he may be harsh they made need that harshness to learn to respect your privacy and be well behaved it's easy when we divorce to be lenient with the children because you feel they have went through enough.
Being a single parent is hard enough without dating, but when you decide the time is right to start dating again you need to be prepared for spreading your time between your family life and your personal life. This may feel like an impossible task, but it can be a lot easier once your children are aware of your intentions of dating and getting married, but this doesn't mean telling them every detail. Your children have had your attention to themselves for some time and may not welcome the thought of having to share your time and affections with others. This is the time to offer them reassurance and give them time to adjust to the idea of you dating. You must let a bond form naturally between them, otherwise bitter feelings could form. It is vital that you understand how your children are feeling. It will be necessary to keep reassuring them that you aren't going anywhere and you will always be there for them, but don't let them stop you from being happy if this man makes you happy and doesn't harm your children physically then I don't see anything wrong with a little discipline. Communication is very important right now so talk to him and ask him to be more patient with the children and that it bothers you that he is so harsh with them at times.
You're welcome and remember this is just as much an adjustment for your children as it is for you and your boyfriend and as long as he is not harming them physically and not verbally abusing them but is disciplining them it's okay they may actually respect him more for being that other father figure. Try asking your children how they feel about your boyfriend and then take it from there if they say they like him but he is too hard on them then talk to him but if they say they like him without saying he is mean then he may be doing the right thing as hard as it may be to accept. If they say he is too mean and they are afraid of him then talk to him and tell him to ease up a bit.