Keep your expectations at zero. It was nice of you to send your h birthday greetings, but he may or may not recognize your text today. Some day, he may mention it. I know you are disappointed, but try not to focus on it. You did what you would normally do for anyone that is celebrating their special day.
As for whether he's celebrating his birthday or not...who knows and right now...you don't need to worry about it. When your mother questioned him about today, he may have lied to her just so that it would get back to you...again, not your circus to deal w/today. Your mother apparently loves the drama and wants to be all up in the middle of it. I think you did the right thing by telling her that you didn't want to hear about what he's doing, etc. Set your boundaries w/her, i.e., the less you tell her the better.
You are doing well...don't allow the MLC train to derail your plans for the day.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.