Your dc are not "jealous" of your relationship with your dp, but they are fearful that it will cause you to devote all of your attention to him and, effectively, cause you to abandon them as their df, with whom they only have sporadic contact, has done.
They need to learn that, far from diminishing the attention you give them, your relationship will double the attention they currently receive as they'll have another loving and caring adult to whom they can turn to for fun/games/comfort/advice/encouragement and all of the other positives we endeavour to bring to the lives of our dc.
When your dp fetches up once a week make it a special event. Turn the tv off. Dine en famille. Get the board games out/teach them to play cards and be fulsome in praise of their ability to win as well as lose. If your dp is a dab hand in the kitchen get him doing the cooking with your dc as his sous-chefs while you sit and mumsnet knit and if not, make it pizza/tex mex/chinese or similar night where they get to choose what they want to eat or order from the take-away/home delivery service.
Encourage him to build his own bond with your boys; if he's unable to think of how he can achieve this ditch him without further ado as a man who's lacking in imagination won't enchance their, or your, lives in any way.
If his weekly visit to your home becomes a looked forward to event, they'll soon be lamenting his absence and be clamouring to see more of him.
I suggest you make the move to him staying overnight in the neutral ground of a hotel/self-catering holiday in the UK or abroad where they'll become accustomed to seeing him last thing at night and first thing in the morning, but be sure to book in a child-friendly resort where there'll be plenty of activities for them to participate in with and without you, and don't engage in canoodling overt displays of affection in front of them until they have fully accepted him as being part and parcel of their lives with you.
In short, your dp is not just wooing you; he's also courting your boys and he needs to be as assiduous in winning their approval as if he were seeking to win your hand from a particularly disapproving protective df.
Don't underestimate your dc; they look out for you just as much as you look out for them and if they give your dp their approval you'll know you've found a good man.