you say you only get such a short span of time with yor DD each week.
instead of you trying to spend time with your DS, and your DH spending time with DD...can you try to anipulate activities so that you're spending time as a 4.
So, with the ball game for example, instead of trying to get her to play just with DH, say that both you AND DH will play with her. course, chances are she won't be thrilled, and probably will try to exclude DH. but then its on you - as the 'common ground' as it were - to bring DH back in to it. Pass the ball to him, keep him involved, get him passing it to her....get DS involved too.
You could always try planning a few 'family' activities for these times, too. something which might need 4 jobs doing... planting a little vegetable patch, maybe? if she sees that everybody has an important role, DH and DS will start to become less redundant in her mind. maybe DH can be in charge of digging, DS might be clearing the soil, you might be planting the seeds, and DH can be 'chief waterer'. With time, she should get more used to DH, and more comfortable with leaving you. you can then start to try and pair off, but still very much with a 'family' stance... maybe a sports day. So that all are involved, once again. you could play children vs grown ups, or, as things progress, mummy and DS vs Daddy and DH.
The idea is that she gets used to DH through activities which involve both of you. She has the safety net of Mummy, and isnt 'fobbed off' to daddy (not saying she is, thats just how she will see it.) But with you working to involve DH in what you are doing with her, she is forced to acknowledge him as a part of something - even better if you can emphasise to her that he was an important part (like with the planting.... "it couldn't have happened if daddy hadn't helped us dig, DS hadn't helped us clear soil...etc"
Really feel for you, and hope this helps.
It can be so hard to hear a child cry for you. And when you are what they want, it's even harder to say no. But cuddling her when shes crying for you (even if it's been 20 mins) just shows her that, eventually, it will give her what she wants. the crying is working, hence she's persevering. Instead of cddling her, perhaps try distracting her. suggest baking a cake (as a family!). if she refuses, get on and do it anyway, with DS and DH. She will see that she's missing out, and the crying didn't work this time...
let me know if you think you can use any of this, and also how you get on.
good luck, and persevere!