I have written a paper together with a co-author. The co-author is a former assistant of mine. The paper is based on my idea but they have done quite a bit of work on it. We had a generally good relationship. The paper has been rejected twice and in the third attempt there was a request for a major revision. I have updated the paper after the rejections, but after the last decision, namely the revision request, the co-author has stated that they want to add some material that they think will likely satisfy the reviewers. I actually know this material and think that it may make another paper, however I said "that's fine by me". This was half a year ago. I am now waiting for the co-author to do what they have promised to do. I am very keen on having the paper published, and I believe that what the reviewers want could be addressed in a different way. I think I could do it (and if it doesn't work submit elsewhere where I think we have better chances with the paper as it is - rejections up to now may have been caused simply by aiming too high). I'm open to what my co-author proposed, so if they did that work, I'd be OK with it as well. However we are losing time and new relevant literature comes out in the meantime, so our task will be more difficult if we wait for much longer.
The thing is, I have asked my co-author a few times how they get on with the work and when we can resubmit. Originally there were answers like "I'll have this done in a week or so", but now they have become unresponsive (last response was end November). I'm starting to doubt that they will ever finish this, and even if they did, I don't think I should wait for very long, one more month OK, but a year or two? No way.
I assume nothing serious has happened because they were active on social media a few days ago.
What are my options now? I could update the paper and tell them that here it is and if I don't hear anything within a week, I take it as a confirmation that it is fine for them if I resubmit it. Would that be OK? I suspect it isn't, but I am interested on views on that.
Note that I already have sent them an email asking for whether it would be OK if I update the paper and resubmit, but I didn't get a response.
An alternative is to remove their name as co-author, rather state in an Acknowledgement what they have done, and submit with only myself as author. Fur sure I do not want to remove their name and I'd warn them about it and offer them to submit with both names if they agree on submission (rather than holding things up for ages), however I wonder if in case I don't hear anything from them using only my name would be the more legally correct option.
Or am I just stuck and there's no way to get this published without a further response from the co-author which might not come?
PS: Additionally I wonder for how long a journal is likely to accept (or at least review) a requested revision. They haven't set us a deadline but it's half a year ago now, so I'm worried.