I'm just going to jump in and add my thoughts on this.
I suspect the main reason Richard II never had any children with Anne of Bohemia was due to Anne of Bohemia herself, as she is from the same Luxembourg generation as Sigismund and Wenceslaus, and that generation only produced 1 legitimate child which was Sigismund's daughter, while there is nothing to suggest the Plantagenets had any fertility problems.
So we can assume Richard would have children with Isabella. If he has a son, then Richard's line is secure, but a daughter could really make things interesting.
If there needed to be a regency for Richard's son, it would almost certainly be Edward of Norwich, who would act as the regent, like everybody has said.
In terms of Richard's position, if Bollingbrooke dies Richard is actually in a brilliant position. Edward of Norwich is his close ally and friends, and won't go against Richard in the TL. Edmund of Langley is getting old and without bollingbrooke would likely remain aligned with Richard, as he has no direct reason to lead a revolt against the king himself. The mortimers are headed up by a minor and are so incredibly unambitious that their chances of succeeding the throne are practically zero, if Richard has no issue. Henry of Monmouth had a brilliant relationship with Richard II in OTL, which will almost certainly remain, and in fact may be even better in this TL as Richard might become his father figure, so Henry will definetley stay loyal. Henry's brothers generally followed what Henry did and had a great relationship with him so they will also likely stay loyal.
Humphrey, Thomas of Woodstock's son is also under Richard's control.
The only legitimate Plantagenet that could lead a rebellion against Richard II is Richard of Consiburgh, but even then that is incredibly unlikely. The only way I think it could happen is if Edward of Norwich gains too much control over Richard in a way that leads to poor governenance, or if Noriwch becomes regent and Conisburgh doesn't gain any more land as the brothers did not have the best relationship.
The remaining members of the Lord's Appellant may immensley dislike Richard, but they lack the power of influence to lead a successful rebellion against him.
Also Owain Glyndwr will never revolt in this TL as his revolt in OTL was due to Bollingbrooke's usurpation and the Percies won't revolt either meaning there should much less civil strife.
Richard with an incredibly popular young Henry of Monmouth to uphold his regime, instead of the unpopular John of Gaunt, may actually be able to implement his policies that he was planning on in OTL.
As to foregin policy I suspect Richard will keep his OTL for the moment but when the Armagnac-Burgundian Civil War properly flares up, Richard may be pressured or perhaps see an opportunity to engage in France, although maybe not to the same level as Henry V in OTL, which in the long term could actually be a good thing for the English.
I also suspect that Richard may focus on Ireland like he did in OTL and try to continue expanding English control over in Ireland, while they wait for the French situation to flare up.