Can a mother keep the kids from their father?

my partner has 2 children to his ex, we have them every 2nd weekend and any other extra time we can spend with them and he also pays his child support. his ex seems to always stir up trouble through sending text messages phone calls and emails which has been going on for a while now. i told my partner he needs to put his foot down and tell her to basically 'f off' because if its not one thing its something else she will whinge that their daughter needs new school shoes because they got scuff marks after being at our house and just other juvenile stuff but it is becoming really annoying, my partner ignores her messages and phone calls and i said to him why doesnt he just tell the b.s has got to stop and he replied to me 'because then she will say i cant see the kids'. thats not fair on him or children and im wanting to know if there is anything he can do and what his rights are.