I love MamaBug's suggestion on how to explain to your kids - I've been worrying about this now that my daughter is almost 9 and asking questions. I'm also newly DX with BP - for decades I've thought it was just depression (I heard that's not uncommon...).

Anyway, to your question about fostering a strong bond. Trippin had an excellent suggestion - making time to do something she loves one-on-one with her, and then including her in something you love. My daughter (and my almost 5-year-old son) both love cooking with us, though dad's better at doing it. They also love nail painting. My husband is really good about doing things with the kids, and I see it all the time in their bond. I'm not as good (I don't have as much patience and am more responsible for scheduling & such, so I don't have as much time to spend as he does on cooking, for example - he does it on his days off, so it doesn't matter if it takes another 10 or 15 minutes).

I will say that 4 years old sounds just about right for the "I want someone else" stage. My kids wanted whomever they weren't with at this stage...could be they're telling dad or grandma the same thing about wanting to be with you. It passed for us in about 6 months or so. I usually just said something like, "You have fun with *whomever*, don't you...but right now we're together and we need to/can do X, Y Z." And move on.

Also, as she gets into preschool, find out who she likes spending time with and see if you can make some playdates with those friends. That was not something that I was used to, until other parents asked me. I don't make friends with or even talk to strangers easily; but having the kids play together gave me an opportunity to get to know them and make some good friends that way. Finally, you might see if there's a local gymnastics place or something where you can do a Mommy & Me class, or even something like swimming, art, soccer - I know that can be hard when you're parenting with an unwilling partner, but even if you just go when you have her, you can meet other families with like interests.