I'd give him the benefit of the doubt really at such an early stage. It may be that his break up was prolonged and painful and he's wary of getting too deep with someone new too quickly, or he may be "busy" with his teenage children who he presumably still sees quite a lot - there may be limited days when his kids aren't staying at his. Only a year after divorce isn't much time to have got over it all and be ready to be serious with a new love interest. What are his work commitments, what are his hobby/interest commitments. He may be juggling more than people think.
I understand that OP wants to spend more time with the new man, and presumably new man wants to spend more time with OP, but compromise has to be made if things are complicated for him. His children will always come first - perhaps they've taken badly to the divorce and need a lot of attention/care and maybe he's not even told them about his new relationship yet?
When I first met my now DH, he was glacially slow and I got very frustrated as he just wouldn't spend the kind of time with me that I wanted and wouldn't commit to dates etc in advance. It was so bad that after 2/3 months, a different bloke started sniffing around me and I ended up seeing them both at the same time for a few weeks, the new guy was a lot more available, and I was seeing him 3/4 dates per week against first guy's one per week. I eventually gave first guy an ultimatum that I needed to see him more, or we were through. He couldn't so that was it. However, new guy only lasted a few months as the initial excitement quickly wore off and I realised I didn't actually like him that much and it was only his availability that I was craving, so I ditched him. Luckily first guy was still "on the scene" in the background, we didn't date during that period, but we still talked and saw eachother in non dating occasions, and we ended up back together and I think it knocked some sense into him, in that we started seeing over 2/3 times per week instead of once. Still not enough for me, after a year of knowing each other, but it was a compromise I could accept for the greater good. Now been together 38 years! He eventually opened up and explained why he was wary of committing too much at the early stages of a new relationship (past awful break up, family, work etc) which were entirely reasonable and I wish he'd spoken out a lot earlier - he was basically scared of getting stung again, and had a lot going on in the background with his parents and work - all genuine.
OP probably needs a few serious heart to heart talks with her new man to help her understand why he only wants to see her once a week. There may be genuine reasons, or he may just be stringing her along. But second guessing is not good. Get the facts and be assertive.