Night shift

[Ropbob]

Can my employer force me to move to night shift if I have a 3 years and 5 years old kids and I'm still breastfeeding one of them?

Are you in the UK? Do you have contracted hours?If you are amd you do then your employer can't force you to do a different shift from your contracted hours and they can't force you to do nights.

What was your original contract?
From the job advert to the inverview to the written contract?
Did it cover working shifts or was it always a day role?
How long have you worked days?
Is this a change in shift patterns or will you be only on nights?

What does your contract say? If it states your current hours (day shifts presumably) then they can't change it without changing your contract. However if it says that you will work x number of hours on any shift (or words to that effect) they can. If that is the case you can submit a flexible working request to only work days but they don't have to accept it if it wouldn't work for the business. This isn't that uncommon for shift work as if everyone with children asks for the day shifts, they'll struggle to find someone willing to do just nights. More common is they'll agree to fixed shifts.
If your contract is for only day shifts they can change it but not without consulting you first and you can refuse. If you refuse they would need to either honour your existing contract or offer you redundancy, and in the case of the latter would need to show that your role as contracted no longer exists.