My girlfriend comes home at 3-4 in the morning

Am 30 yrs old and my partner is 22. We have 2 children been together 5 yrs.
Things have been great between us and we have been in some bad times, but our relationship has always been strong.
Anyway 2 months ago my girlfriend stated coming home from a night out at 3-4 in the morning and most recently 6 am. She used to go out and come home at a normal time like 12 am but I think 4 am is to much.
I have never wanted her to feel traped in our relationship so have never minded her going out. She says am boring and like staying in but I worry about money and also like it at home.
Anyway when she comes home at 4 am we argue. She says whats wrong with it and does not see why its a problem.
There was a time when she was out on Sunday night and did not take the house key. I let her know in a text at 1 am that she must come home as i have work in the at 7 in morning and I must wait up for her to let her in. She came back at 4 am as normal and I missed work. She did say sorry and only goes out once ever 2 weeks but how can I make her know its wrong to come in at that time. Anyway that is one problem.
I fear she might have cheated on me. 1 month and a half ago she went to Spain with he brother and sister to see there mum who lives there. I took 2 weeks off work to take care of the kidds. Anyway when she came back from Spain she told me she met a friend of her brothers. He was the one who introduced them. She said her mother and herself were with this Spanish lad at a bar and her mother went home at 4 am leaving the two off them[ Spanish lad and my girlfriend] ,so they went to benidorm for rest off the night and she did not get home till 4 pm.
This made me suspicios so i checked her phone and found 2 saved text from him and his phone number. Nothing to give suspicion was in the text just a good night kiss. I asked her about him and she said he is just a friend.
I also have always trusted her and love so tried to put it behind me.
Anyway 2 weeks after my girlfriend came back from Spain she said she wants to go back to spain to see her mum. I said I was feeling suspicious and don't want her to go but she convinced me that the Spanish lad was at the other side of the country visiting his mother for 1 month. My girlfriends mother has him round as a friend so told my girlfriend this. I still did not want her to go but she did anyway.
So 2 weeks after my partner came back from Spain the 1st time she was off again 3 week
later for 3 weeks..When she came back from Spain the 2nd time it was a Thursday night. I went to bed for work and had not seen her much. I come home from work next day[Friday] and 2 hours later she was going out for the night. I thought she would want to be with me seen as she ain't seen me for 3 weeks.
That same night my partners sister phoned me and said she has just been on the phone to Emma[my partner who was in a bar] asking how her holiday was. Emma told her sister she had a row with her mother and she went and stayed at this Spanish lads house for the night.
Emma and her sister have always got on and i could not understand why she would lie about this so i decided my worst nightmare has come true and Emma has been cheating.I was gutted.
I asked Emma about this and she says her sister is lieing. Emma mother also said the same.
So I dont have proof but it looks like it.
We had a row and I lashed out brusing her forehead.
I was wrong to do and feel bad.We don't have a violent relationship. Now she says she want to split up and maybe we can date again when we have time apart.
I find this hard to deal with. I mean if we are to split up then i need time to get over her but to be thinking we might get back together is stoping the healing proccess.
Wost still for the time being we are in the same house but its a calm atmosphere.
I love her and would love us to be a couple. She also says she loves me.
Is our relationship doomed and am i being nieve to think i need proof off her cheating.
I don't know what to do and feel its all a mess.
Pleeeeeese give me your advice as am a broken man.
Thx

Your patner was only seventeen when you met. She has never had time to be young like you, as you were eight years ahead. She needs that period now. Stay in the family but give her the freedom she needs. She loves you and the children need their family. Do not control her and go to sleep when she is out. When she has explored what she missed when she was young, she will come back to you and be happy that you are still there. Concentrate on the children and on other interests for a while.