Oh this was SO my daughter! I stay at home too and she was and still is VERY attached to me, especially around that 2 y/o age. She just turned 4 and honestly, just within the last few months have I noticed her gravitating more towards Daddy. That's not to say it's been as extreme as it once was between 2 and 4, but literally within the last 2 months is the first time EVER that she's asked Daddy to put her to bed while I'm at home.
I would also suggest just leaving the house. I know that doesn't sound all that appealing since you really just want downtime to sit down or load the dishwasher or whatever, but my husband used to come home and on particularly rough days would say...don't you have to get gas?! So, I did, and then I went to Starbuck's! ;)
It will get better. For us we mostly just let her cry and fuss about it during one activity and then I'd help for the other activity. For instance dad would give her bath and then I'd get her in jammies and put her to bed. Eventually he was able to do both bath and jammies and I came in at the end. Now I still usually am the one to put her to bed but she has no problems with me being in the house and not tending to her every need! Lots of people told me one day she'll switch to Daddy, but, and not to make it worse ;), but that day hasn't happened yet!
This is a frustrating time! I hear you! Hang in there! It does get better, slowly but surely!