Hi D.. First I'm going to start with your last statement about needing to work. That's just the guilt that we usually feel as working mothers. No need to feel guilty about that. That just shows your boys how it is to be a productive woman, and they will have a healthy appreciation for women once they get older and understand her need to work, or maybe just her desire to do so, once they get old enough to appreciate it.
As for the bonding situation, yes it is important for boys to bond with their fathers, but it's just as important for them to bond with their mothers. You are the one to set the example for the type of women they are likely to be most attracted to in the future. You are the model that they base their interactions with women on.
You're trying too hard, and the anxiety that you're feeling is coming through to them, and so maybe they're feeling smothered by the attention that you're trying to give them instead of relaxed. Kids pick up on the smallest vibes from us and act accordingly. Have you ever tried participating in the activities that they share with their father? Stop thinking that this is a competition between the two of you for their attention. Just relax and just be!!! That's the best advice I can give you. Just be mom and enjoy your sons, and you will see that they will start to gravitate more to you. Just make the time that you spend with them a natural encounter, and things will get better.
Most of all STOP the guilty feelings because we don't need to be around our children 24 hours a day for them to appreciate us as parents. I truly hope, no I KNOW that things will work out for you. Talk to your husband about how you're feeling, and go on family outings when possible so that you can see how relaxed he is with them.
Take care of yourself and R-E-L-A-X!!!