Why would you have a child with someone who doesn't want a child?
That's moot really. When the ovaries take over from the brain, the outcomes are not necessarily to everyone's liking. The point is, the OP wants another child and it's obviously less important to her that DH doesn't. Just to clarify, what OP is doing here is trying to get pregnant and at the same time, acknowledging that her DH doesn't want a child and if he doesn't, he, not her, needs to stop having unprotected sex and sort some contraception.
Ass-covering in other words.
On the face of it, she has a point ime, as long as she's taken into account the following very real possibilities, and others we cannot know:
a) She could be left looking after three on her own, with the emotional, financial etc implications of that
b) He could get the snip unbeknownst to her
c) They could have a third and his resentment and the strain it puts them under could result in them splitting up
If she accedes to his wishes and doesn't have another child, her resentment over that and sadness over not having a child she wants could result in everything going tits up anyway.
Six of one, half dozen of the other ime. Plenty go into relationships and have children, and with the best will in the world, it all goes pear-shaped anyway.