Did she answer any of your texts last night?
if you don;t answer your mobile today, depending on how maudlin you were last night, she will probably phone the land line to check you are ok.
All you can do is say you apologise for dumping your woes on her, you were very upset and crying (omit the drink) and couldn't see clearly to text properly. That you aren;t up to seeing anyone today, your head is a lot clearer and you want to get the housework out of the way because you have things to do next week with regard to moving forward with your life.
I dare say she will phone her mother first, to get your DHs side of the story.
Don't admit to drunk texting, you don't need that feeding back if there could be any sort of residency case in the future. Never give any ammunition to the other side.
If she's likely to just drop round unannounced, because you're texts were of a 'life isn't worth living' nature - make sure you hide the bottles because you do not want it feeding back that you're sitting in alone getting pissed in charge of a child.
Hope you are feeling a bit better this morning, we all do stupid things sometimes. Just make sure you do some damage limitation 