Thing is - If Tess's DH is busy telling his DD that it will all be fine, Tess will do it all, she doesn't have to worry...then why would Tess's DD think any different. TBH I don't think this is now centered on Tess's dsd, I think it now HAS to be centred on her DH and how much he is willing to step up and be a supportive parent...And a supportive husband to Tess. He needs to stop ignoring Tess's views on rearing her dsd's baby, and stop discounting the work that Tess does.
Tess's DH has categorically stated that he will not put his DD into a mother and baby unit, and has told his DD that she can keep the baby. All on the assumption that his life will carry on much the same as before, Because Tess will do all the hard work. That, IMO, is at best unfair, and at worst, doing his DD a great disservice, as there is no way she will learn to cope with her baby if she is not made to/helped to.
There will be plenty of services out there to help Tess's dsd, surely it is time for Tess to stop running around and doing all the hard work, and insisting that her DH AND her dsd (who's baby it will be, after all) find out about the services available to make sure it does not fall to Tess.
Tess - Tell your DH that he needs to help his DD to do practical things, like booking in with a MW. DON'T do it for them...