As long as you are divorced, there is no problem getting married again. It's up to you whether you choose to go down the route of Retained Rights or if you choose to apply for a right of residence through your fiance, whichever you feel would be easier.
However if you are not married with your partner, a right of residence is not automatic and depends on your personal circumstances. The Home Office likes to see proof of co-habitation for 2 years for unmarried partners, though if you have children you could argue your way around it, though it might have to be in appeal court as the Home Office might refuse if you have co-habited for less than 2 years. If your partner has a PR certificate, you will not have to prove that she is currently exercising Treaty rights, otherwise you will have to.
For Retained Rights you will need proof that your ex-wife was exercising Treaty rights throughout the divorce proceedings from start to finish. If you can't, it may be possible to appeal and ask the court to make
directions to the Home Office to check the HMRC records of your ex-wife for proof of exercising of Treaty rights.