I'm in a similar situation, although further down the line - been with DP for four years and he was widowed ten years ago. Ten year anniversary came up recently and I gave a bit of space on the day as he wanted to go to the graveside and spend time looking through photos with his daughter.
I find that it's not hard, exactly, but I have to make a bit of mental space for it - I didn't meet DP and his daughter until years after their loss, so it doesn't impinge on me and on our relationship, but I have to take it into account.
I know what you mean about feeling second best, but that's not what I feel, no more than DP feels second best to my ex-husband. That's just a feeling, not a fact, and it's not that helpful. Having said that, it's totally normal and human! If you were to talk to him about it (probably not on the anniversary!), would he be ready to have that conversation?
I have found in dating a widower that I have had to learn to be more patient and more accommodating, but also to insist on being treated properly and making sure he is being a good boyfriend to me. We split up several times in the first couple of years while he worked through his guilt about finding someone new and disbelief that I could really love him when he felt so damaged, but we're doing great now. I had to be quite strong and sure about what I wanted and was prepared to put up with.
It's quite early days for both of you, relationship-wise and grief-wise. Patience will probably help but it's hard on you.