Having affair

Hi
Joined this site just now as I have no-one to talk to about this and really just need to get things off my chest and know that someone will at least read it.
Background, I have been with my partner 10 years and have two children aged 1 and 4. And I know this a cliche but my children are everything to me and I would do anything for them, although I know people will doubt this once they read my story. We own our own house and car, joint accounts etc. We are both mid/ late 30s.
My partner is beautiful and a wonderful mother/ housekeeper, I really can't fault her in any way and I do love her, but now I am seriously doubting whether I am still in love with her.
Plus the physical side of our relationship has never been really great and this is a big thing for me. I am the only man she has ever slept with and her first and only boyfriend. I know I should have said something earlier in our relationship but I just got caught up in the whirlwind of her being taken in by my family and me by hers and before I knew it we had bought a house and planning children. I think now I saw her as a friend rather than a lover. Marriage had never been a big issue for either of us.
I on the other hand had slept with many women before I met her and loved and needed sex. We used to have it maybe once/ twice a week in the early days but over the last few years this really did dry up. We have tried talking about it. I have tried to introduce things like sexy lingerie etc which I really like on a woman, but she is not interested and thinks I'm perverted. Sex has always been a 'get it over with' type of thing with her and she says herself she's not a 'sex' person.
We then decided to have children and I had been with her that long I felt how could I deny her? But I admit once she fell pregnant I was as excited as anything.
Since our first child was born the sex stopped almost completely, which I accepted as she was a new mother. Then it only started again when we decided that we wanted to have another child. At first I wasn't sure about having another child, but I let my sense of how could I deny my partner another child and my 1st child a sibling take over. Trying for our second child, the sex really was just a reproductive act, barely any kissing or affection. I am as much to blame for this as her as in the end I wasn’t really trying to make it anything special, as I had in a way given up on having any sort of exciting sexual relationship with her.
Anyway our second child was born 12 months ago and we have not had any intimacy with each other in all that time, or the 9 months previous to the birth. Again I had just sort of accepted this was how my life was going to be, but then it happened.
I work in a nighttime job and met a woman (I’ll call her X) and we slept together that night and it was amazing. She had been in an unhappy relationship and within a week of me meeting her she had finished with her boyfriend.
To cut a long story short we have now been seeing each other regularly for nearly 6 months. We have an amazing sex life, something I thought I would never feel again with anyone. We go on out of town dates so she can be affectionate with me in public and me with her and also have nights in in her flat. It just feels incredible and electric when I’m with her, like nothing I’ve ever felt before. I am freelance/ self employed and it’s easy to have an excuse for seeing her when my partner thinks I’m working.
Plus we have fallen in love with each other and told each other that although we both knew we had. Yet I have always told X that I can’t leave my children. X understood things at first, but things have become so intense that now she feels she cannot wait for me and although she loves me, she wants more and needs to move on and just wishes it was with me. She tells me it kills her that we have no real future. Of course I can’t blame her for this at all and I feel the same. I stress she is not asking me to leave my family, but now just feels as though we should end what we have as it can't go anywhere long term. Plus it is not just sex with her; we have created a genuine emotional bond with each other over time. Plus the thought of her going into the arms of someone else makes me feel sick.
This has now hit me hard and although I can’t bear the thought of leaving my family I also cannot bear the thought of not being with X either. After experiencing what I have with X the thought of going back to an affectionless relationship fills me with dread. I would always want to be there for my children when they wake up etc, but know this wouldn’t be possible if I chose the other option. I’ve been trawling the net looking at relationship advice forums and stuff and advice on how children are affected by parents splitting up. Plus my partner would be shattered and it would really affect our extended family as well.
I have been completely emotionally and physically drained recently living what is in effect a double life. (I’m not looking for sympathy though and know I won’t get it). And today I’ve hit a low point after seeing X last night. I haven’t slept or eaten today and have been crying, asking myself what have I become.
Again I’m not looking for sympathy, just needed to get this all out and let someone say something to me, shout at me, whatever.
Thanks for reading