So sorry to hear of your situation, I can't believe men do this when women are at their most vulnerable! My XH started an affair when I was 4 months pregnant with our second child, told me about it when she was 3 weeks old and moved out 2 weeks later. Know that it is not your fault and make sure you lean on your family and friends for the emotional support you need.
Financially, the CSA would say he has to give you 20pc of his salary for 2 children. However, he may be reasonable and give you more at this stage while the children are young, but that is for you to discuss. My X paid the mortgage as well as giving some living money until we sold the house and I am now renting a smaller and cheaper place. He now probably gives me around 30pc of his salary as with 2 toddlers I am still financially unable to go back to work (although he has access to the children, he is no help at all with actual childcare during working hours!) Also contact child tax credits office to see if there is any help there, and I'd recommend a trip to citizens advice for a chat about any other financial support.
As for access, my x now has the children (now aged 3 1/2 and 2) every other weekend from fri night to Sunday evening. We did try every Friday night and sat day (meaning I had sat night and sun day) every week, but I found he was constantly asking to chop and change due to other plans, and it made me mad! This way we each get a weekend with them plus a weekend to ourselves so no excuses for cutting into their time.
It is harder when they are tiny, I was still Breastfeeding so for the first 6 months he had to visit rather than take them both away for the day. I would leave him in the living room with them and have a nap or go to tescos. I think this was every weekend. And he'd pop in a couple of times a week at bedtime on his way back from work too. He first had them overnight when baby was 6 months old and I'd stopped Breastfeeding. It was hard for me but I went away with some friends so I didn't think about it as much! Then we did the every sat thing, and now we're onto every other weekend. He's also supposed to come once a week after work and take them out for an hour but it doesn't always work as he can't leave early. It just has to be what works for you all - let him take them off for an afternoon and have some time to yourself or go for lunch with friends.
And really really do not blame yourself. It is not your fault. I am still fuming 2 years later - my divorce has just been finalised. He is still with other woman (10 yrs younger than me and him, typical midlife crisis!) Sex was something that he went on about too - sorry to disappoint the guys but being pregnant is not always that fun, even more so when you have a toddler to chase about too! I am now with a lovely man who looks after us, so please know that things will get better. Xx