Firstly, have you actually sold the house? You'll need to negotiate with your buyers if contracts have been exchanged, as all plants should remain as their property unless listed separate as NOT being part of the sale.

You can dig up both primroses and violets and pot them up now, so that they root in the pots and you can plant them into your new garden. The tree is obviously more vulnerable - if it's small enough to plant into a large pot, then do that...otherwise, you'll have to chat to your buyers, get into your new house and prepare a hole, then go back and remove the tree into a sack with as much rootball as you can, and plant it ASAP. Don't forget to water it well for the first year.

I hope this helps and you're not moving too far to make the 2nd option impossible!