I'd say just do your best to make them feel like you enjoy them. Give lots of hugs, tell them how much you love em. If you absolutely cannot get out of bed, let them know it's not them and you're sorry. It would be ok imo to say you're sad about work or something. And change the subject, ask all about their day. I think you're right to not mention bp at this point. People have used that against each other in custody battles.
The thing with fake it til you make it - it really can work. Forced smiles & laughter & positive self talk can retrain your subconscious mind. Helped me get better for sure. I'm a much better mom now with my 3rd. And I'm so grateful for that. I've also done a lot of healing and rebonding with my older 2. It's all possible.