Can ex wife claim even though i have residency?

My exwife and i divorced over 12 years ago. She left the marital home after it was discovered she was having an affair. We have four children together. At the time they were 1,2,3 & 6. She had the children in her care at the marital home for a few weeks but found them to much to cope with as she was quite young still herself. So i moved in to take on the care of the children. As time went on my ex then decided that she wanted to move back into the marital home and re take on the care of the children. Cut a long story short things did go badly and it ended in court and i was granted residency with her having over night access if wished. I was not working at the time and she was only lowpaid income. We managed to come to a amicable agreement to do with the children. She had access to them whenever she wished, i even agreed to her coming back into the maritall home to spend time with the children as she was only in a caravan. As time went on i myself met and married my present partner who i have now been with for 10 yrs and we have a 1 year old between us and my ex is engaged to and living with her partner on the same estate. The children are now 12,14,15 and 18. sometimes have been difficult with the children as they have gotten older, but all 4 adults have tried to come togther and sort any issues. My ex does give the children more of a free reign than i do and i don't agree with every aspect of what she lets the children do while in her care but i don't have right to tell her what can and can't happen in her own home. The eldest son last year went to live with his mother on a permenant basises as he didn't like rules set down in our home when at his mothers he doesn't really have any.right to say what does and doesn't go on in her home. Recently the 2 middle children have been getting themselves into a bit of trouble both in and out of school amongst other things. They have been staying with their mother on a more regular basis and i don't like what i am hearing about from people. I hear stories of them drinking and smoking even while in the presence of their mother at her home. We have had a fallout over the children recently and the middle 2 children are refusing to come back to my home. Alot of things go on when over there. every time there is an issue with anything the stories start coming out but always with different ones so it's never really known whats true or lies or just exaggerated so can't be acted upon. The children do play us all off against each to get what they want sometimes. what i need to get help and advice with now is how the money situation should go and what rights my exwife has to do with these matters. She claims to have been "housing" the children for the last 6 months. the children have been allowed to come and go to their mothers house as they please, and to be honested i do think thy majority of the time they wish to be there as they come and go as they please and bring whoever into the house when they want. My wife and i can't run our house like that. If the children are with us the fuss will get kicked up as we are not as leanient as their mother with them. I want to try to get advice with the rights she has and the rights the children have in the desicion making of a situation like this. I know they are all teenagers now and i can't force them to come back to our home. the youngest has expressed a wish to remain living permanently with my wife and myself but the 2 middle children now refuse to come back basically because they don't like the way they have to abide by any rules we set. Even though i was granted residency i never had a penny off my ex wife. It was agreed to could she see the children whenever she wanted. I agreed to this as i believed no matter what was wrong between herself and me, the children should not suffer as a result of this and still needed 2 loving parents even when not together, Her partner and herself both work full time in good management position jobs, i am self employed but trade is very slow for me at the moment so business is not at its best. My wife as yet is not in work due to the baby as we would not be able to afford childcare as yet. My exwife has now expressed that she is wishing to put in a claim for all benefit rights to do with the children plus i think a matinence claim from myself. I have no idea if she is entitled to do this or not so would really appreciate any advice anyone can offer. I don't know what is said in regards to me andmy present wife while the children are in the care of their mother i hear some many different things, especially from my youngest boy who is closer to his stepmother rather than his own mother. He is always coming back from his mothers house feeling like he is being victimised by herself her partner and they rest of the children as he prefers to be in our home rather than theirs. I really am in a situation now that i'm not sure how to handle in the best way so i'm REALLY REALLY desperate for anything anybody maybe able to tell me on hows best to try to sort this situation. Thanks!!